0,7

Number of permutations satisfying -k<=p(i)-i<=r, i=1..n-4, with k=1, r=4. - Vladimir Baltic (baltic(AT)matf.bg.ac.yu), Jan 17 2005

a(n)=number of compositions of n-4 with no part greater than 5. Example: a(12)=61 because we have 61 compositions of 8: 8=1+1+1+1+1+1+1+1=2+1+1+1+1+1+1=...=2+2+1+1+1+1=...=2+2+2+1+1=...=2+2+2+2 =3+1+1+1+1+1=...=3+2+1+1+1=...=3+2+2+1=...=3+3+1+1=...=3+3+2=... =4+1+1+1+1=...=4+2+1+1=...=4+2+2=...=4+3+1=...=5+1+1+1=...=5+2+1=...=5+3=3+5 - Vladimir Baltic (baltic(AT)matf.bg.ac.yu), Jan 17 2005

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

I. Flores, k-Generalized Fibonacci numbers, Fib. Quart., 5 (1967), 258-266.

V. E. Hoggatt, Jr. and M. Bicknell, Diagonal sums of generalized Pascal triangles, Fib. Quart., 7 (1969), 341-358, 393.

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.4.

T. D. Noe, Table of n, a(n) for n=0..200

Joerg Arndt, Fxtbook

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 12

Eric Weisstein's World of Mathematics, Fibonacci n-Step Number

Eric Weisstein's World of Mathematics, Pentanacci Number

x^4/(1 - x - x^2 - x^3 - x^4 - x^5)

G.f.: 1/(1-z-z^2-z^3-z^4-z^5) . (S.Plouffe) [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 17 2009]

A001591:=-1/(-1+z+z**2+z**3+z**4+z**5); [Conjectured by S. Plouffe in his 1992 dissertation.]

g:=1/(1-z-z^2-z^3-z^4-z^5): gser:=series(g, z=0, 49): seq((coeff(gser, z, n)), n=-4..32); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 17 2009]

CoefficientList[Series[x^4/(1 - x - x^2 - x^3 - x^4 - x^5), {x, 0, 50}], x]

Row 5 of arrays A048887 and A092921 (k-generalized Fibonacci numbers).

Sequence in context: A006775 A104993 A128761 this_sequence A003240 A018487 A010747

Adjacent sequences: A001588 A001589 A001590 this_sequence A001592 A001593 A001594

nonn

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 16 2000