A029360 Expansion of 1/((1-x^4)*(1-x^7)*(1-x^8)*(1-x^10)).

1, 0, 0, 0, 1, 0, 0, 1, 2, 0, 1, 1, 2, 0, 2, 2, 3, 1, 3, 2, 4, 2, 4, 3, 6, 3, 5, 4, 8, 4, 7, 6, 10, 5, 9, 8, 12, 7, 12, 10, 15, 9, 15, 12, 18, 12, 18, 15, 22, 15, 22, 18, 26, 18, 26, 22, 31, 22, 31, 26, 36, 26, 36, 31, 42, 31, 42

Offset

0,9

Comments

Number of partitions of n into parts 4, 7, 8, and 10. - Hoang Xuan Thanh, May 15 2026

Links

Table of n, a(n) for n=0..66.

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

Formula

G.f.: 1/((1-x^4)*(1-x^7)*(1-x^8)*(1-x^10)).

a(n) = floor((n+20)*(n^2+34*n-12)/13440 - (n mod 2)*(n-1)*(n+30)/640 + ((n^2+n+2) mod 4)*n/64 + ((3*n^3+n^2+2*n+4) mod 7)/7 + (131*((n+3) mod 4) + 26*((n+1) mod 4) - 35*(n mod 4))/640). - Hoang Xuan Thanh, May 15 2026

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^7)(1-x^8)(1-x^10)), {x, 0, 100}], x] (* Harvey P. Dale, Apr 25 2015 *)

Prog

(PARI) Vec(1/((1-x^4)*(1-x^7)*(1-x^8)*(1-x^10)) + O(x^90)) \\ Hoang Xuan Thanh, May 15 2026

Crossrefs

Sequence in context: A374521 A202177 A354793 * A337541 A185279 A088432

Adjacent sequences: A029357 A029358 A029359 * A029361 A029362 A029363

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved