A029328 Expansion of 1/((1-x^4)*(1-x^5)*(1-x^6)*(1-x^9)).

1, 0, 0, 0, 1, 1, 1, 0, 1, 2, 2, 1, 2, 2, 3, 3, 3, 3, 5, 4, 5, 5, 6, 6, 8, 7, 8, 9, 10, 10, 12, 11, 13, 14, 15, 15, 18, 17, 19, 20, 22, 22, 25, 24, 27, 29, 30, 30, 34, 34, 37, 38, 40, 41, 46, 45, 48, 50, 53, 54, 59, 58, 62, 65

Offset

0,10

Comments

Number of partitions of n into parts 4, 5, 6, and 9. - 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 (0,0,0,1,1,1,0,0,0,-1,-1,0,-1,-1,0,0,0,1,1,1,0,0,0,-1).

Formula

G.f.: 1/((1-x^4)*(1-x^5)*(1-x^6)*(1-x^9)).

a(n) = a(n-4)+a(n-5)+a(n-6)-a(n-10)-a(n-11)-a(n-13)-a(n-14)+a(n-18)+a(n-19)+a(n-20)-a(n-24). - Wesley Ivan Hurt, Apr 22 2021

a(n) = floor((n^3+36*n^2+420*n+2248)/6480 - (n mod 2)*(n+6)/48 + ((2*n^2+1) mod 3)*(3*n+41)/162 - ((2*n^2+2*n) mod 3)*17/162 + ((4*n^3+4*n^2+2) mod 5)/5). - Hoang Xuan Thanh, Apr 16 2026

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^5)(1-x^6)(1-x^9)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 11 2020 *)

Prog

(PARI) Vec(1/((1-x^4)*(1-x^5)*(1-x^6)*(1-x^9)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 16 2026

Crossrefs

Sequence in context: A181834 A194848 A289497 * A109831 A247352 A097266

Adjacent sequences: A029325 A029326 A029327 * A029329 A029330 A029331

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved