A029329 Expansion of 1/((1-x^4)*(1-x^5)*(1-x^6)*(1-x^10)).

1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 3, 1, 2, 1, 3, 3, 4, 2, 4, 3, 7, 4, 6, 4, 8, 7, 9, 6, 10, 8, 14, 9, 13, 10, 16, 14, 18, 13, 19, 16, 25, 18, 24, 19, 28, 25, 31, 24, 33, 28, 40, 31, 40, 33, 45, 40, 49, 40, 52, 45, 61, 49, 61, 52

Offset

0,11

Comments

Number of partitions of n into parts 4, 5, 6, and 10. - Hoang Xuan Thanh, Apr 16 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,-1,0,-1,0,0,-1,0,-1,0,0,1,1,1,0,0,0,-1).

Formula

a(n) = floor((n^3+45*n^2+468*n+2240)/7200 - (n mod 2)*(n^2+25*n)/480 + ((3*n^2+3) mod 5)*n/50 + ((3*n^3+n^2+4*n+4) mod 5)/5). - Hoang Xuan Thanh, Apr 16 2026

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^5)(1-x^6)(1-x^10)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 11 2020 *)
LinearRecurrence[{0, 0, 0, 1, 1, 1, 0, 0, -1, 0, -1, 0, 0, -1, 0, -1, 0, 0, 1, 1, 1, 0, 0, 0, -1}, {1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 3, 1, 2, 1, 3, 3, 4, 2, 4, 3, 7, 4, 6, 4, 8}, 80] (* Harvey P. Dale, Dec 15 2021 *)

Prog

(PARI) Vec(1/((1-x^4)*(1-x^5)*(1-x^6)*(1-x^10)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 16 2026

Crossrefs

Sequence in context: A090270 A326441 A178830 * A287872 A191863 A166866

Adjacent sequences: A029326 A029327 A029328 * A029330 A029331 A029332

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved