A029362 Expansion of 1/((1-x^4)*(1-x^7)*(1-x^8)*(1-x^12)).

1, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 3, 0, 1, 2, 4, 0, 1, 3, 5, 1, 2, 4, 7, 1, 3, 5, 9, 2, 4, 7, 11, 3, 5, 9, 14, 4, 7, 11, 17, 5, 9, 14, 20, 7, 11, 17, 24, 9, 14, 20, 28, 11, 17, 24, 33, 14, 20, 28, 38, 17, 24, 33, 44, 20, 28, 38

Offset

0,9

Comments

Number of partitions of n into parts 4, 7, 8, and 12. - Hoang Xuan Thanh, May 16 2026

Links

Table of n, a(n) for n=0..67.

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

Formula

a(n) = floor((n+43)*(n^2-7*n+481)/16128 - (n mod 2)*(n^2+31*n+576)/768 + ((n^2+n+2) mod 4)*(n^2+31*n)/768 + ((n^2+3*n+2) mod 4)*n*7/768 - ((n^3+3*n) mod 4)/2). - Hoang Xuan Thanh, May 16 2026

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^7)(1-x^8)(1-x^12)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 11 2020 *)
LinearRecurrence[{0, 0, 0, 1, 0, 0, 1, 1, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, -1}, {1, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 3, 0, 1, 2, 4, 0, 1, 3, 5, 1, 2, 4, 7, 1, 3, 5, 9, 2, 4}, 70] (* Harvey P. Dale, Jan 21 2024 *)

Prog

(PARI) Vec(1/((1-x^4)*(1-x^7)*(1-x^8)*(1-x^12)) + O(x^90)) \\ Hoang Xuan Thanh, May 16 2026

Crossrefs

Sequence in context: A390662 A297617 A351982 * A216599 A114510 A325466

Adjacent sequences: A029359 A029360 A029361 * A029363 A029364 A029365

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved