A029307 Expansion of 1/((1-x^3)*(1-x^7)*(1-x^8)*(1-x^10)).

1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 6, 5, 6, 7, 7, 7, 9, 9, 9, 10, 11, 11, 12, 13, 14, 14, 16, 16, 17, 18, 19, 20, 21, 22, 24, 24, 26, 27, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 45, 47

Offset

0,11

Comments

Number of partitions of n into parts 3, 7, 8, and 10. - Hoang Xuan Thanh, Apr 09 2026

Links

Table of n, a(n) for n=0..64.

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

Formula

a(n) = floor((n^3+42*n^2+564*n+3042)/10080 - (n mod 2)*n/160 - (n mod 3)/9 + ((n^3+n^2+n+1) mod 4)/8 + ((4*n^3+2*n+2) mod 7)/7 + (((n+7) mod 8) - (n mod 8))/16). - Hoang Xuan Thanh, Apr 09 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^7)(1-x^8)(1-x^10)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 12 2020 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^7)*(1-x^8)*(1-x^10)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 09 2026

Crossrefs

Sequence in context: A339186 A302479 A029355 * A161066 A161105 A048165

Adjacent sequences: A029304 A029305 A029306 * A029308 A029309 A029310

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved