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

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.

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

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

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