A029012 Expansion of 1/((1-x)*(1-x^2)*(1-x^5)*(1-x^7)).

1, 1, 2, 2, 3, 4, 5, 7, 8, 10, 12, 14, 17, 19, 23, 26, 30, 34, 38, 43, 48, 54, 60, 66, 73, 80, 88, 96, 105, 114, 124, 134, 145, 156, 168, 181, 194, 208, 222, 237, 253, 269, 287, 304, 323, 342, 362, 383, 404, 427, 450

Offset

0,3

Comments

Number of partitions of n into parts 1, 2, 5, and 7. - Joerg Arndt, Oct 15 2014

Links

Table of n, a(n) for n=0..50.

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

Formula

G.f.: 1/((1-x)*(1-x^2)*(1-x^5)*(1-x^7)).

a(n) = floor((2*n^3+45*n^2+298*n+956)/840+(-1)^n/16). - Tani Akinari, Oct 15 2014

Mathematica

CoefficientList[Series[1/((1 - x) (1 - x^2) (1 - x^5) (1 - x^7)), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 15 2014 *)

Prog

(Magma) [Floor((2*n^3+45*n^2+298*n+956)/840+(-1)^n/16): n in [0..60]]; // Vincenzo Librandi, Oct 15 2014
(PARI) Vec(1/((1-x)*(1-x^2)*(1-x^5)*(1-x^7)) + O(x^80)) \\ Michel Marcus, Oct 15 2014

Crossrefs

Sequence in context: A325512 A211858 A349149 * A095699 A112192 A017841

Adjacent sequences: A029009 A029010 A029011 * A029013 A029014 A029015

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved