A029314 - OEIS

A029314

Expansion of 1/((1-x^3)*(1-x^7)*(1-x^10)*(1-x^12)).

1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 2, 0, 2, 2, 1, 2, 2, 2, 2, 3, 3, 3, 4, 3, 5, 4, 4, 6, 5, 5, 7, 7, 6, 8, 9, 7, 10, 10, 9, 11, 12, 11, 13, 14, 13, 15, 16, 15, 18, 18, 18, 20, 21, 20, 23, 24, 23, 26, 27, 26, 30, 30, 30, 33, 34, 33, 37

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,11

COMMENTS

Number of partitions of n into parts 3, 7, 10, and 12. - Hoang Xuan Thanh, Apr 12 2026

LINKS

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

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

FORMULA

a(n) = floor((n^3+48*n^2+864*n+1134)/15120 - (n mod 2)*(n+114)/240 - ((2*n^2+n) mod 3)*n/36 + ((5*n^3+2*n^2+n+1) mod 7)/7 + (1-(floor(n/5) mod 2))*((n^4+4*n^3+2*n^2+n+4) mod 5)/5 + (floor(n/5) mod 2)*((4*n^4+3*n^3+4*n^2+4*n+2) mod 5)/5). - Hoang Xuan Thanh, Apr 12 2026

MATHEMATICA

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

PROG

(PARI) Vec(1/((1-x^3)*(1-x^7)*(1-x^10)*(1-x^12)) + O(x^50)) \\ Hoang Xuan Thanh, Apr 12 2026

CROSSREFS

Sequence in context: A384195 A360022 A118206 * A071635 A156643 A378972

Adjacent sequences: A029311 A029312 A029313 * A029315 A029316 A029317

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane

STATUS

approved