A029331 - OEIS

A029331

Expansion of 1/((1-x^4)*(1-x^5)*(1-x^6)*(1-x^12)).

1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 3, 1, 2, 2, 4, 3, 4, 2, 5, 4, 6, 4, 8, 5, 7, 6, 10, 8, 11, 7, 12, 10, 14, 11, 17, 12, 16, 14, 21, 17, 22, 16, 24, 21, 27, 22, 31, 24, 31, 27, 37, 31, 39, 31, 42, 37, 46, 39, 52, 42, 52, 46

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OFFSET

0,11

COMMENTS

Number of partitions of n into parts 4, 5, 6, and 12. - Hoang Xuan Thanh, Apr 19 2026

LINKS

Table of n, a(n) for n=0..63.

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

FORMULA

a(n) = floor((n^3+48*n^2+694*n+7830)/8640 - (n mod 2)*(n^2+27*n)/576 + (((n+2) mod 4) - (n mod 4))*n/192 + (((n+5) mod 6) - ((n+3) mod 6))*n/216 + (((n+3) mod 4) - 5*(n mod 4))/32). - Hoang Xuan Thanh, Apr 19 2026

MATHEMATICA

CoefficientList[Series[1/((1-x^4)(1-x^5)(1-x^6)(1-x^12)), {x, 0, 70}], x] (* Harvey P. Dale, Nov 25 2014 *)

PROG

(PARI) Vec(1/((1-x^4)*(1-x^5)*(1-x^6)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 11 2020

CROSSREFS

Sequence in context: A342655 A161901 A102862 * A037269 A124579 A035306

Adjacent sequences: A029328 A029329 A029330 * A029332 A029333 A029334

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved