A029041 Expansion of 1/((1-x)*(1-x^3)*(1-x^5)*(1-x^9)).

1, 1, 1, 2, 2, 3, 4, 4, 5, 7, 8, 9, 11, 12, 14, 17, 18, 20, 24, 26, 29, 33, 35, 39, 44, 47, 51, 57, 61, 66, 73, 77, 83, 91, 96, 103, 112, 118, 126, 136, 143, 152, 163, 171, 181, 194, 203, 214, 228, 238, 251, 266, 277, 291, 308, 321, 336, 354, 368, 385, 405

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of partitions of n into parts 1, 3, 5, and 9. - Alois P. Heinz, Oct 01 2014

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1,1,-1,0,-1,2,-1,0,-1,1,-1,1,0,1,-1).

Programs

Mathematica

CoefficientList[Series[1/((1-x)(1-x^3)(1-x^5)(1-x^9)), {x, 0, 90}], x] (* Jinyuan Wang, Mar 24 2020 *)

PARI

a(n)=round((n+9)*(n^2+18*n+52)/810+(n\3+1)*(3*!(n%3)-1)/27+[12,-5,-10][n%3+1]/81) \\ Tani Akinari, May 23 2014

PARI

a(n)=(n^3+27*n^2+204*n+700+10*[3*n+29,4,0][n%3+1])\810 \\ Tani Akinari, Oct 01 2014

PARI

Vec(1/((1-x)*(1-x^3)*(1-x^5)*(1-x^9)) + O(x^80)) \\ Michel Marcus, Oct 01 2014

Formula

a(n) = floor((n^3+27*n^2+204*n+700+10*[3*n+29,4,0][(n mod 3)+1])/810). - Tani Akinari, Oct 01 2014

a(n) = 1 + floor((n^3+27*n^2+204*n+30*n*[(n mod 3)=0])/810) where [] is Iverson bracket. - Hoang Xuan Thanh, Jun 09 2025