A029097 Expansion of 1/((1-x)*(1-x^5)*(1-x^8)*(1-x^10)).

1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 5, 5, 5, 6, 6, 8, 9, 9, 11, 11, 14, 15, 15, 17, 18, 21, 23, 23, 26, 27, 31, 33, 34, 37, 39, 43, 46, 47, 51, 53, 59, 62, 64, 68, 71, 77, 81, 83, 89, 92, 100, 104, 107, 113, 117, 125, 131, 134

Offset

0,6

Comments

Number of partitions of n into parts 1, 5, 8 and 10. - Ilya Gutkovskiy, May 21 2017

Links

Table of n, a(n) for n=0..57.

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

Formula

a(n) = floor((2*n^3+72*n^2+673*n+2160)/4800 + n*(-1)^n/320 + ((4*n^2+n+2) mod 5)*n/50 + ((n^3+2*n+4) mod 5)/5). - Hoang Xuan Thanh, Feb 26 2026

Prog

(PARI) Vec(1/((1-x)*(1-x^5)*(1-x^8)*(1-x^10)) + O(x^60)) \\ Hoang Xuan Thanh, Feb 26 2026

Crossrefs

Sequence in context: A228571 A224908 A386288 * A210955 A051697 A240869

Adjacent sequences: A029094 A029095 A029096 * A029098 A029099 A029100

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved