A029040 Expansion of 1/((1-x)(1-x^3)(1-x^5)(1-x^8)).

1, 1, 1, 2, 2, 3, 4, 4, 6, 7, 8, 10, 11, 13, 15, 17, 20, 22, 25, 28, 31, 35, 38, 42, 47, 51, 56, 61, 66, 72, 78, 84, 91, 98, 105, 113, 121, 129, 138, 147, 157, 167, 177, 188, 199, 211, 223, 235, 249, 262, 276, 291, 305

Offset

0,4

Comments

a(n) is the number of partitions of n into parts 1, 3, 5, and 8. - Joerg Arndt, Jan 18 2017

Links

Table of n, a(n) for n=0..52.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,1,-1).

Formula

G.f.: 1/((1-x)*(1-x^3)*(1-x^5)*(1-x^8)).

a(n) = floor((2*n^3+51*n^2+384*n+1368+180*(1+(-1)^floor((n+1)/2))*(-1)^floor(n/4))/1440). - Tani Akinari, Jun 28 2013

Mathematica

CoefficientList[Series[1/((1 - x) (1 - x^3) (1 - x^5) (1 - x^8)), {x, 0, 100}], x] (* Wesley Ivan Hurt, Jan 17 2017 *)

Prog

(PARI) a(n)=(2*n^3+51*n^2+384*n+1368+(1+(-1)^((n+1)\2))*(-1)^(n\4)*180)\1440 \\ Charles R Greathouse IV, Jun 28 2013

Crossrefs

Sequence in context: A239950 A077768 A143038 * A053281 A339395 A228117

Adjacent sequences: A029037 A029038 A029039 * A029041 A029042 A029043

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved