A029185 Expansion of 1/((1-x^2)*(1-x^4)*(1-x^7)*(1-x^12)).

1, 0, 1, 0, 2, 0, 2, 1, 3, 1, 3, 2, 5, 2, 6, 3, 8, 3, 9, 5, 11, 6, 12, 8, 15, 9, 17, 11, 21, 12, 23, 15, 27, 17, 29, 21, 34, 23, 37, 27, 43, 29, 47, 34, 53, 37, 57, 43, 64, 47, 69, 53, 77, 57, 83, 64, 92, 69, 98, 77, 108, 83

Offset

0,5

Comments

a(n) is the number of partitions of n into parts 2, 4, 7, and 12. - Hoang Xuan Thanh, Oct 11 2025

Links

Table of n, a(n) for n=0..61.

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

Formula

a(n) = floor((n^3+48*n^2+636*n+2078)/4032 - (n^2+25*n+133)*(n mod 2)/192 + (n+14)*((n^2+n+2) mod 4)/96 + ((3*n^3+4*n^2+4*n+4) mod 7)/7). - Hoang Xuan Thanh, Oct 11 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^4)(1-x^7)(1-x^12)), {x, 0, 70}], x] (* or *) LinearRecurrence[{0, 1, 0, 1, 0, -1, 1, 0, -1, 0, -1, 1, 1, -1, 0, -1, 0, 1, -1, 0, 1, 0, 1, 0, -1}, {1, 0, 1, 0, 2, 0, 2, 1, 3, 1, 3, 2, 5, 2, 6, 3, 8, 3, 9, 5, 11, 6, 12, 8, 15}, 70] (* Harvey P. Dale, May 15 2016 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^4)*(1-x^7)*(1-x^12)) + O(x^70)) \\ Hoang Xuan Thanh, Oct 11 2025

Crossrefs

Sequence in context: A029240 A302642 A025803 * A029184 A179049 A341976

Adjacent sequences: A029182 A029183 A029184 * A029186 A029187 A029188

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved