A029367 Expansion of 1/((1-x^4)*(1-x^7)*(1-x^10)*(1-x^12)).

1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 2, 0, 2, 1, 2, 1, 2, 2, 3, 2, 3, 2, 5, 2, 4, 3, 6, 3, 5, 5, 7, 4, 7, 6, 9, 5, 9, 7, 11, 7, 11, 9, 13, 9, 13, 11, 16, 11, 16, 13, 19, 13, 19, 16, 22, 16, 22, 19, 26, 19, 26, 22, 30, 22, 30, 26, 34

Offset

0,13

Comments

Number of partitions of n into parts 4, 7, 10, and 12. - Hoang Xuan Thanh, Jun 19 2026

Links

Table of n, a(n) for n=0..68.

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

Formula

a(n) = floor((n^3+60*n^2+876*n+7632)/20160 - (n mod 2)*(n^2+33*n+308)/960 + ((n^2+n+2) mod 4)*(n+12)/96 + ((2*n^3+n^2+2*n+4) mod 7)/7). - Hoang Xuan Thanh, Jun 19 2026

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^7)(1-x^10)(1-x^12)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 11 2020 *)

Prog

(PARI) Vec(1/((1-x^4)*(1-x^7)*(1-x^10)*(1-x^12)) + O(x^80)) \\ Hoang Xuan Thanh, Jun 19 2026

Crossrefs

Sequence in context: A049115 A294204 A329697 * A192541 A281545 A332033

Adjacent sequences: A029364 A029365 A029366 * A029368 A029369 A029370

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved