%I A001519 M1439 N0569
%S A001519 1,1,2,5,13,34,89,233,610,1597,4181,10946,28657,75025,196418,514229,1346269,
%T A001519 3524578,9227465,24157817,63245986,165580141,433494437,1134903170,
%U A001519 2971215073,7778742049,20365011074,53316291173,139583862445,365435296162
%N A001519 a(n) = 3a(n-1)-a(n-2), with a(0) = a(1) = 1.
%C A001519 If the initial term is deleted, this is a bisection of the Fibonacci
sequence A000045.
%C A001519 Number of ordered trees with n+1 edges and height at most 3 (height=number
of edges on a maximal path starting at the root). Number of directed
column-convex polyominoes of area n+1. Number of nondecreasing Dyck
paths of length 2n+2. - Emeric Deutsch (deutsch(AT)duke.poly.edu),
Jul 11 2001
%C A001519 Terms for n>1 are the solutions to : 5x^2-4 is a square. - Benoit Cloitre
(benoit7848c(AT)orange.fr), Apr 07 2002
%C A001519 a(1) = 1, a(n+1) = smallest Fibonacci number greater than the n-th partial
sum. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Oct 21 2002
%C A001519 The fractional part of tau*a(n) decreases monotonically to zero. - Benoit
Cloitre (benoit7848c(AT)orange.fr), Feb 01 2003
%C A001519 n such that floor(phi^2*n^2)-floor(phi*n)^2 = 1 where phi=(1+sqrt(5))/
2 - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 16 2003
%C A001519 Number of leftist horizontally convex polyominoes with area n+1.
%C A001519 Number of 31-avoiding words of length n on alphabet {1,2,3} which do
not end in 3. (e.g. n=3, we have 111,112,121,122,132,211,212,221,
222,232,321,322 and 332). See A028859. - Jon Perry (perry(AT)globalnet.co.uk),
Aug 04 2003
%C A001519 Appears to give all solutions >1 to the equation : x^2=ceiling(x*r*floor(x/
r)) where r=phi=(1+sqrt(5))/2. - Benoit Cloitre, Feb 24, 2004
%C A001519 a(1) = 1, a(2) = 2, then the least number such that the square of any
term is just less than the geometric mean of its neighbors. a(n+1)*a(n-1)>
a(n)^2. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 06
2004
%C A001519 All positive integer solutions of Pell equation b(n)^2 - 5*a(n)^2 = -4
together with b(n)=A002878(n), n>=0. - W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de),
Aug 31 2004
%C A001519 a(n) = L(n,3), where L is defined as in A108299; see also A002878 for
L(n,-3). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com),
Jun 01 2005
%C A001519 Essentially same as Pisot sequence E(2,5).
%C A001519 Number of permutations of [n+1] avoiding 321 and 3412. E.g. a(3) = 13
because the permutations of [4] avoiding 321 and 3412 are: 1234,
2134, 1324, 1243, 3124, 2314, 2143, 1423, 1342, 4123, 3142, 2413,
2341. - Bridget Eileen Tenner (bridget(AT)math.mit.edu), Aug 15 2005
%C A001519 Number of 1324-avoiding circular permutations on [n+1].
%C A001519 A subset of the Markoff numbers (A002559). - Robert G. Wilson v (rgwv(at)rgwv.com),
Oct 05 2005.
%C A001519 (x,y)=(a(n),a(n+1)) are the solutions of x/(yz)+y/(xz)+z/(xy)=3 with
z=1. - Floor van Lamoen (fvlamoen(AT)hotmail.com), Nov 29 2001
%C A001519 Number of (s(0), s(1), ..., s(2n)) such that 0 < s(i) < 5 and |s(i) -
s(i-1)| = 1 for i = 1,2,....,2n, s(0) = 1, s(2n) = 1. - Herbert Kociemba
(kociemba(AT)t-online.de), Jun 10 2004
%C A001519 With interpolated zeros, counts closed walks of length n at the start
or end node of P_4. a(n) counts closed walks of length 2n at the
start or end node of P_4. The sequence 0,1,0,2,0,5,.. counts walks
of length n between the start and second node of P_4. - Paul Barry
(pbarry(AT)wit.ie), Jan 26 2005
%C A001519 a(n) = number of ordered trees on n edges containing exactly one non-leaf
vertex all of whose children are leaves (every ordered tree must
contain at least one such vertex). For example, a(0) = 1 because
the root of the tree with no edges is not considered to be a leaf
and the condition "all children are leaves" is vacuously satisfied
by the root and a(4) = 13 counts all 14 ordered trees on 4 edges
(A000108) except (ignore dots)
%C A001519 |..|
%C A001519 .\/.
%C A001519 which has two such vertices. - David Callan (callan(AT)stat.wisc.edu),
Mar 02 2005
%C A001519 Number of directed column-convex polyominoes of area n. Example: a(2)=2
because we have the 1 X 2 and the 2 X 1 rectangles. - Emeric Deutsch
(deutsch(AT)duke.poly.edu), Jul 31 2006
%C A001519 Same as the number of Kekule structures in polyphenanthrene in terms
of the number of hexagons in extended (1,1)-nanotubes. See Table
1 on page 411 of I. Lukovits and D. Janezic. - Parthasarathy Nambi
(PachaNambi(AT)yahoo.com), Aug 22 2006
%C A001519 Number of free generators of degree n of symmetric polynomials in 3-noncommuting
variables. - Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Oct 24
2006
%C A001519 Inverse: With phi = (sqrt(5) + 1)/2, log_phi((sqrt(5) a(n) + sqrt(5 a(n)^2
- 4))/2) = n for n >= 1. - David W. Cantrell (DWCantrell(AT)sigmaxi.net),
Feb 19 2007
%C A001519 Consider a teacher who teaches one student, then he finds he can teach
two students while the original student learns to teach a student.
And so on with every generation an individual can teach one more
student then he could before. a(n) starting at a(2) gives the total
number of new students/teachers (see program). - Ben Thurston (benthurston27(AT)yahoo.com),
Apr 11 2007
%C A001519 The Diophantine equation a(n)=m has a solution (for m>=1) iff ceiling(arsinh(sqr(5)*m/
2)/ln(phi)))<>ceiling(arcosh(sqr(5)*m/2)/ln(phi))) where phi is the
golden ratio. An equivalent condition is A130255(m)=A130256(m). -
Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 24 2007
%C A001519 a(n+1)= B^(n)(1), n>=0, with compositions of Wythoff's complementary
A(n):=A000201(n) and B(n)=A001950(n) sequences. See the W. Lang link
under A135817 for the Wythoff representation of numbers (with A as
1 and B as 0 and the argument 1 omitted). E.g. 2=`0`, 5=`00`, 13=`000`,
..., in Wythoff code.
%C A001519 The sequence starting (1, 2, 5, 13,...) = row sums of triangle A140068.
- Gary W. Adamson (qntmpkt(AT)yahoo.com), May 04 2008
%C A001519 Bisection of the Fibonacci sequence into odd indexed non-zero terms (1,
2, 5, 13,...) and even indexed terms (1, 3, 8, 21,...) may be represented
as row sums of companion triangles A140068 and A140069. - Gary W.
Adamson (qntmpkt(AT)yahoo.com), May 04 2008
%C A001519 a(n) = number of partitions pi of [n] (in standard increasing form) such
that Flatten[pi] is a (2-1-3)-avoiding permutation. Example: a(4)=13
counts all 15 partitions of [4] except 13/24 and 13/2/4. Here "standard
increasing form" means the entries are increasing in each block and
the blocks are arranged in increasing order of their first entries.
Also number that avoid 3-1-2. - David Callan (callan(AT)stat.wisc.edu),
Jul 22 2008
%C A001519 Equals row sums of triangle A152251 starting with offset 1. [From Gary
W. Adamson (qntmpkt(AT)yahoo.com), Nov 30 2008]
%C A001519 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 27 2008:
(Start)
%C A001519 Let P = the partial sum operator, A000012: (1; 1,1; 1,1,1;...) and A153463
%C A001519 = M, the partial sum & shift operator. It appears that beginning with
any
%C A001519 randomly taken sequence S(n), iterates of the operations M * S(n), ->
M * ANS,
%C A001519 -> P * ANS,...etc, (or starting with P) will rapidly converge upon a
two-
%C A001519 sequence limit cycle of (1, 2, 5, 13, 34,...) and (1, 1, 3, 8, 21,...).
(End)
%C A001519 Row sums of triangle A153342 = odd indexed Fibonacci numbers. [From Gary
W. Adamson (qntmpkt(AT)yahoo.com), Dec 24 2008]
%C A001519 a(n) = 0.25*(A153266(n) + A153267(n)), apart from initial terms [From
Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Jan 02
2009]
%C A001519 Sum_{n>=0} atan(1/a(n)) = (3/4)Pi [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com),
Feb 27 2009]
%C A001519 Syntactically similar to A001906 in the sense that both have the nth
term t(n) given by t(n) = 3t(n-1) + t(n-2) , for n > 1. [From Kailasam
Viswanathan Iyer (kvi(AT)nitt.edu), Apr 24 2009]
%C A001519 Summation of the squares of fibonacci numbers taken 2 at a time. Offset
1. a(3)=5. [From Al Hakanson (hawkuu(AT)gmail.com), May 27 2009]
%D A001519 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences,
Academic Press, 1995 (includes this sequence).
%D A001519 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973
(includes this sequence).
%D A001519 E. Barcucci, A. Del Lungo, S. Fezzi and R. Pinzani, Nondecreasing Dyck
paths and q-Fibonacci numbers, Discrete Math., 170, 1997, 211-217.
%D A001519 E. Barcucci, R. Pinzani and R. Sprugnoli, Directed column-convex polyominoes
by recurrence relations, Lecture Notes in Computer Science, No. 668,
Springer, Berlin, 1993, pp. 282-298.
%D A001519 A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of
combinatorial proof, M.A.A. 2003, id. 13,15.
%D A001519 S. Brlek, E. Duchi, E. Pergola and S. Rinaldi, On the equivalence problem
for succession rules, Discr. Math., 298 (2005), 142-154.
%D A001519 N. G. de Bruijn, D. E. Knuth and S. O. Rice, The average height of planted
plane trees, in: Graph Theory and Computing (ed. T. C. Read), Academic
Press, New York, 1972, pp. 15-22.
%D A001519 Naiomi T. Cameron and Asamoah Nkwanta, On Some (Pseudo) Involutions in
the Riordan Group, Journal of Integer Sequences, Vol. 8 (2005), Article
05.3.7.
%D A001519 E. Deutsch and H. Prodinger, A bijection between directed column-convex
polyominoes and ordered trees of height at most three, Theoretical
Comp. Science, 307, 2003, 319-325.
%D A001519 A. Gougenheim, About the linear sequence of integers such that each term
is the sum of the two preceding, Fib. Quart., 9 (1971), 277-295,
298.
%D A001519 I. Lukovits and D. Janezic, "Enumeration of conjugated circuits in nanotubes",
J. Chem. Inf. Comput. Sci., vol. 44 (2004) pp. 410-414.
%D A001519 S. Rinaldi and D. G. Rogers, Indecomposability: polyominoes and polyomino
tilings, Math. Gaz., to appear, 2008.
%D A001519 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p.
39.
%D A001519 M. C. Wolf, Symmetric functions of noncommutative elements, Duke Math.
J. 2 (1936), 626-637.
%D A001519 F. Yano and H. Yoshida, Some set partition statistics in non-crossing
partitions and generating functions, Discr. Math., 307 (2007), 3147-3160.
%H A001519 T. D. Noe, <a href="b001519.txt">Table of n, a(n) for n=0..200</a>
%H A001519 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to
linear recurrences with constant coefficients</a>
%H A001519 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al,
1992.
%H A001519 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
1031 Generating Functions and Conjectures</a>, Universit\'{e} du
Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A001519 E. Barcucci, A. Del Lungo, R. Pinzani and R. Sprugnoli, <a href="http:/
/www.mat.univie.ac.at/~slc/opapers/s31barc.html">La hauteur des polyominos...</
a>
%H A001519 N. Bergeron, C. Reutenauer, M. Rosas and M. Zabrocki, <a href="http:/
/arXiv.org/abs/math.CO/0502082">Invariants and Coinvariants of the
Symmetric Group in Noncommuting Variables</a>, to appear Canad. J.
Math.
%H A001519 D. Callan, <a href="http://arXiv.org/abs/math.CO/0210014">Pattern avoidance
in circular permutations</a>.
%H A001519 David Callan, <a href="http://front.math.ucdavis.edu/0802.2275">Pattern
avoidance in "flattened" partitions </a>.
%H A001519 Aleksandar Cvetkovic, Predrag Rajkovic and Milos Ivkovic, <a href="http:/
/www.cs.uwaterloo.ca/journals/JIS/index.html">Catalan Numbers, the
Hankel Transform and Fibonacci Numbers</a>, Journal of Integer Sequences,
Vol. 5 (2002), Article 02.1.3
%H A001519 Enrica Duchi, Andrea Frosini, Renzo Pinzani and Simone Rinaldi, <a href="http:/
/www.cs.uwaterloo.ca/journals/JIS/index.html">A Note on Rational
Succession Rules</a>, J. Integer Seqs., Vol. 6, 2003.
%H A001519 J.-P. Ehrmann et al., <a href="http://forumgeom.fau.edu/POLYA/ProblemCenter/
POLYA003.html">POLYA003: Integers of the form a/(bc) + b/(ca) + c/
(ab)</a>.
%H A001519 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=127">
Encyclopedia of Combinatorial Structures 127</a>
%H A001519 I. Jensen, <a href="http://www.ms.unimelb.edu.au/~iwan/polygons/Polygons_ser.html">
Series exapansions for self-avoiding polygons</a>
%H A001519 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
RecursiveSequences.html">Recursive Sequences</a>
%H A001519 M. Renault, <a href="http://www.math.temple.edu/~renault/fibonacci/thesis.html">
Dissertation</a>
%H A001519 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
FibonacciHyperbolicFunctions.html">Fibonacci Hyperbolic Functions</
a>
%H A001519 D. Zeilberger, <a href="http://arXiv.org/abs/math.CO/9801016">[math/9801016]
Automated counting of LEGO towers</a>
%H A001519 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to
Chebyshev polynomials.</a>
%H A001519 R. Knott, <a href="http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/
fibpi.html">Pi and the Fibonacci numbers</a> [From Jaume Oliver Lafont
(joliverlafont(AT)gmail.com), Feb 27 2009]
%F A001519 G.f.: (1-2x)/(1-3x+x^2).
%F A001519 a(n)=3a(n-1)-a(n-2)=a(1-n).
%F A001519 a(n)=(phi^(2n-1)+phi^(1-2n))/sqrt(5) where phi=(1+sqrt(5))/2. - Michael
Somos, Oct 28 2002
%F A001519 a(n) = A007598(n-1)+A007598(n) = A000045(n-1)^2+A000045(n)^2 = F(n)^2+F(n+1)^2
- Henry Bottomley (se16(AT)btinternet.com), Feb 09 2001
%F A001519 a(n)=sum(binomial(n+k, 2k), k=0..n). - Len Smiley (smiley(AT)math.uaa.alaska.edu),
Dec 09 2001
%F A001519 a(n) ~ (1/5)*sqrt(5)*phi^(2*n+1) - Joe Keane (jgk(AT)jgk.org), May 15
2002
%F A001519 a(1)=1, a(2)=2, a(n+2)=(a(n+1)^2+1)/a(n) - Benoit Cloitre (benoit7848c(AT)orange.fr),
Aug 29 2002
%F A001519 a(n) = Sum(k=0, n, C(n, k)*F(k+1)) - Benoit Cloitre (benoit7848c(AT)orange.fr),
Sep 03 2002
%F A001519 Let q(n, x)=sum(i=0, n, x^(n-i)*binomial(2*n-i, i)); then q(n, 1)=a(n)
(this comment is essentially the same as that of L. Smiley) - Benoit
Cloitre (benoit7848c(AT)orange.fr), Nov 10 2002
%F A001519 a(n) = (1/2)*(3*a(n-1)+sqrt(5*a(n-1)^2-4)) - Benoit Cloitre (benoit7848c(AT)orange.fr),
Apr 12 2003
%F A001519 Main diagonal of array defined by T(i, 1)=T(1, j)=1, T(i, j)=Max(T(i-1,
j)+T(i-1, j-1); T(i-1, j-1)+T(i, j-1)) - Benoit Cloitre (benoit7848c(AT)orange.fr),
Aug 05 2003
%F A001519 Hankel transform of A002212. E.g. Det([1, 1, 3;1, 3, 10;3, 10, 36])=
5 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 25 2004
%F A001519 Solutions x > 0 to equation floor(x*r*floor(x/r)) = floor(x/r*floor(x*r))
when r=phi - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 15 2004
%F A001519 a(n)=sum(i=0, n, binomial(n+i, n-i)) - Jon Perry (perry(AT)globalnet.co.uk),
Mar 08 2004
%F A001519 a(n)= S(n, 3) - S(n-1, 3) = T(2*n+1, sqrt(5)/2)/(sqrt(5)/2) with S(n,
x)=U(n, x/2), resp. T(n, x), Chebyshev's polynomials of the second,
resp. first kind. See triangle A049310, resp. A053120. - W. Lang
(wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 31 2004
%F A001519 a(n)= ((-1)^n)*S(2*n, I), with the imaginary unit I and S(n, x)=U(n,
x/2) Chebyshev's polynomials of the second kind, A049310. - W. Lang
(wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 31 2004
%F A001519 a(n)=sum_{0<=i_1<=i_2<=n}binomial(i_2, i_1)*binomial(n, i_1+i_2) - Benoit
Cloitre (benoit7848c(AT)orange.fr), Oct 14 2004
%F A001519 a( n ) = a( n - 1 ) + SUM[ i = 0 to n - 1 ] a( i ) a( n ) = Fib( 2n +
1 ) SUM[ i = 0 to n - 1 ] a(i) = Fib( 2n ) - Andras Erszegi (erszegi.andras(AT)chello.hu),
Jun 28 2005
%F A001519 The i-th term of the sequence is the entry (1, 1) of the i-th power of
the 2 by 2 matrix M=((1, 1), (1, 2)). - Simone Severini (ss54(AT)york.ac.uk),
Oct 15 2005
%F A001519 a(n-1)=(1/n)*sum_{k=0...n}B(2k)*F(2n-2k)*binomial(2n, 2k) where B(2k)
is the (2k)-th Bernoulli number - Benoit Cloitre (benoit7848c(AT)orange.fr),
Nov 02 2005
%F A001519 a(n) = A055105(n,1)+A055105(n,2)+A055105(n,3) = A055106(n,1)+A055106(n,
2) - Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Oct 24 2006
%F A001519 a(n)=2/sqrt(5)*cosh((2n-1)*psi), where psi=ln(phi) and phi=(1+sqrt(5))/
2. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Apr 24 2007
%F A001519 a(n) = (phi+1)^n - phi*A001906(n) with phi=(1+sqrt(5))/2. - Reinhard
Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 22 2007
%F A001519 a(n) = 2*a(n-1)+2*a(n-2)-a(n-3); a(n) = (sqrt(5.0) + 5.0)/10.0*(3.0/2.0
+ sqrt(5.0)/2.0)^(n-2) + (-sqrt(5.0) + 5.0)/10.0*(3.0/2.0 - sqrt(5.0)/
2.0)^(n-2). - Antonio A. Olivares (olivares14031(AT)yahoo.com), Mar
21 2008
%F A001519 a(n)=A147703(n,0). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov
29 2008]
%F A001519 a(n) = -a(n-1)+11*a(n-2)-4*a(n-3), this formula (it is one of two 3rd
order linear recurrence relations given for this sequence) is a result
of the generating floretion Z = X*Y with X = 1.5'i + 0.5i' + .25(ii
+ jj + kk + ee) and Y = 0.5'i + 1.5i' + .25(ii + jj + kk + ee). [From
Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Jan 02
2009]
%F A001519 With X,Y defined as X = ( F(n) F(n+1) ), Y = ( F(n+2) F(n+3) ), where
F(n) is the nth Fibonacci number (A000045), it follows a(n+2) = X.Y'
, where Y' is the transpose of Y (n >= 0). [From Kailasam Viswanathan
Iyer (kvi(AT)nitt.edu), Apr 24 2009]
%e A001519 a(3)=13: there are 14 ordered trees with 4 edges; all of them, except
for the path with 4 edges, have height at most 3.
%p A001519 count:=0; node:=proc(g) global count; for j from 1 to g do for i from
0 to (g-j) do node(j-1); end do; end do; count:=count +1; end proc;
- Ben Thurston (benthurston27(AT)yahoo.com), Apr 11 2007
%p A001519 A001519:=-(-1+z)/(1-3*z+z**2); [S. Plouffe in his 1992 dissertation.
Gives sequence without an initial 1.]
%t A001519 Fibonacci /@ (2Range[29] - 1) (from Robert G. Wilson v (rgwv(at)rgwv.com),
Oct 05 2005)
%o A001519 (PARI) a(n)=fibonacci(2*n-1)
%o A001519 (PARI) a(n)=real(quadgen(5)^(2*n))
%o A001519 (PARI) a(n)=subst(poltchebi(n)+poltchebi(n-1),x,3/2)*2/5
%o A001519 (Other) sage: [lucas_number1(n,3,1)-lucas_number1(n-1,3,1) for n in xrange(0,
30)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 29
2009]
%Y A001519 Cf. A000045. First differences of A001906 and of A055588. a(n)= A060920(n,
0).
%Y A001519 Row 3 of array A094954.
%Y A001519 Equals A001654(n+1) - A001654(n-1), n>0.
%Y A001519 Cf. A001653. A122367 is another version.
%Y A001519 Cf. A055105, A055106, A055107, A074664, A124292, A124293, A124294, A124295.
%Y A001519 Cf. inverse sequences A130255 and A130256.
%Y A001519 Cf. A140068, A140069.
%Y A001519 A152251 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 30 2008]
%Y A001519 Cf. A153342, A153463.
%Y A001519 Cf. A153266, A153267 [From Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de),
Jan 02 2009]
%Y A001519 Sequence in context: A141448 A011783 A122367 this_sequence A048575 A099496
A114299
%Y A001519 Adjacent sequences: A001516 A001517 A001518 this_sequence A001520 A001521
A001522
%K A001519 nonn,nice,easy,core
%O A001519 0,3
%A A001519 N. J. A. Sloane (njas(AT)research.att.com).
%E A001519 Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Aug 24 2006,
May 13 2008
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