0,8

a(n-5) is the number of ways of throwing n with an unstated number of standard dice and so the row sum of A061676; for example a(9)=8 is the number of ways of throwing a total of 4: 4, 3+1, 2+2, 1+3, 2+1+1, 1+2+1, 1+1+2 and 1+1+1+1; if order did not distinguish partitions (i.e. the dice were indistinguishable) then this would produce A001402 instead. - Henry Bottomley (se16(AT)btinternet.com), Apr 01 2002

Number of permutations satisfying -k<=p(i)-i<=r, i=1..n-5, with k=1, r=5. - Vladimir Baltic (baltic(AT)matf.bg.ac.yu), Jan 17 2005

a(n)=number of compositions of n-5 with no part greater than 6. Example: a(12)=63 because we have 63 compositions of 7: 7=1+1+1+1+1+1+1=2+1+1+1+1+1=...=2+2+1+1+1=...=2+2+2+1=...=3+1+1+1+1=... =3+2+1+1=...=3+2+2=...=3+3+1=...=4+1+1+1=...=4+2+1=...=4+3=3+4=5+1+1 =1+5+1=1+1+5=5+2=2+5=6+1=1+6 - Vladimir Baltic (baltic(AT)matf.bg.ac.yu), Jan 17 2005

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

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

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 13

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.

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

Eric Weisstein's World of Mathematics, Hexanacci Number

x^5/(1 - x - x^2 - x^3 - x^4 - x^5 - x^6)

A001592:=-1/(-1+z+z**2+z**3+z**4+z**5+z**6); [S. Plouffe in his 1992 dissertation.]

CoefficientList[Series[x^5/(1 - x - x^2 - x^3 - x^4 - x^5 - x^6), {x, 0, 50}], x]

Row 6 of arrays A048887 and A092921 (k-generalized Fibonacci numbers).

Sequence in context: A145112 A062259 A001949 this_sequence A140134 A049886 A128901

Adjacent sequences: A001589 A001590 A001591 this_sequence A001593 A001594 A001595

nonn,easy

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

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