0,3

Inverse binomial transform of powers of 5 (A000351) preceded by 0. - Paul Barry (pbarry(AT)wit.ie), Apr 02 2003

Number of walks of length n between any two distinct vertices of the complete graph K_5. Example: a(2)=3 because the walks of length 2 between the vertices A and B of the complete graph ABCDE are: ACB, ADB, AEB. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004

The terms of the sequence are the number of segments (sides) per iteration of the space-filling Peano-Hilbert curve. - Giorgio Balzarotti (greenblue(AT)tiscali.it), Mar 16 2006

General form: k=4^n-k. Also: A001045, A078008, A097073, A115341, A015518, A054878 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]

Index entries for sequences related to linear recurrences with constant coefficients

a(n)=4^n/5-(-1)^n/5. E.g.f. (exp(4x)-exp(-x))/5. - Paul Barry (pbarry(AT)wit.ie), Apr 02 2003

a(n)=sum{k=1..n, binomial(n, k)(-1)^(n+k)*5^(k-1) }. - Paul Barry (pbarry(AT)wit.ie), May 13 2003

a(2n) = 4*a(2n-1) -1, a(2n+1) = 4*a(2n) +1. In general this is true for all sequences of the type a(n) +a(n+1) = q^(n): i.e. a(2n) = q*a(2n-1) -1 and a(2n+1) = q*a(2n) +1. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 15 2003

a(n)=4^(n-1) - a(n-1). G.f.=x/(1-3x-4x^2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004

a(n+1)=sum{k=0..floor(n/2), binomial(n-k, k)3^(n-2k)4^k} - Paul Barry (pbarry(AT)wit.ie), Jul 29 2004

a(n)=4a(n-1)-(-1)^n, n>0, a(0)=0. - Paul Barry (pbarry(AT)wit.ie), Aug 25 2004

a(n)=Sum_{k, 0<=k<=n}A155161(n,k)*2^(n-k), n>=1 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 27 2009]

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=3*a[n-1]+4*a[n-2]od: seq(a[n], n=0..33); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 15 2008]

g:=1/(1+4*z): gser:=series(g, z=0, 43): seq(abs(coeff(gser, z, n)-1)/5, n=0..31); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 09 2009]

k=0; lst={k}; Do[k=4^n-k; AppendTo[lst, k], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]

a(-1)=0 sage: from sage.combinat.sloane_functions import recur_gen2b sage: it = recur_gen2b(1, 3, 3, 4, lambda n: 0) sage: [it.next() for i in xrange(0, 24)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 03 2008

(Other) sage: [lucas_number1(n, 3, -4) for n in xrange(0, 24)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]

Cf. A015518, A001045.

Cf. A001045, A078008, A097073, A115341, A015518, A054878 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]

Sequence in context: A016064 A163774 A014985 this_sequence A146279 A098619 A086608

Adjacent sequences: A015518 A015519 A015520 this_sequence A015522 A015523 A015524

nonn,easy

Olivier Gerard (olivier.gerard(AT)gmail.com)