A029287 Expansion of 1/((1-x^3)*(1-x^5)*(1-x^9)*(1-x^11)).

1, 0, 0, 1, 0, 1, 1, 0, 1, 2, 1, 2, 2, 1, 3, 3, 2, 3, 4, 3, 5, 5, 4, 6, 6, 6, 7, 8, 7, 9, 10, 9, 11, 12, 11, 13, 15, 13, 16, 17, 16, 19, 20, 19, 22, 24, 22, 26, 27, 26, 30, 31, 30, 34, 36, 35, 39, 40, 40, 44, 46, 45, 49, 52, 51, 56, 58, 57, 62, 65, 64, 69, 72, 71

Offset

0,10

Comments

Number of partitions of n into parts 3, 5, 9, and 11. - Vincenzo Librandi, Jun 04 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = floor((n^3+42*n^2+639*n+1296)/8910 - ((2*n^2+2*n) mod 3)*n/27 + ((2*n^3+4*n^2+3*n+2) mod 5)/5 + ((3*n^3+5*n^2+3*n+5) mod 11)/11). - Hoang Xuan Thanh, Mar 31 2026

Mathematica

CoefficientList[Series[1/((1 - x^3) (1 - x^5) (1 - x^9) (1 - x^11)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 04 2014 *)
LinearRecurrence[{0, 0, 1, 0, 1, 0, 0, -1, 1, 0, 1, -1, 0, -2, 0, -1, 1, 0, 1, -1, 0, 0, 1, 0, 1, 0, 0, -1}, {1, 0, 0, 1, 0, 1, 1, 0, 1, 2, 1, 2, 2, 1, 3, 3, 2, 3, 4, 3, 5, 5, 4, 6, 6, 6, 7, 8}, 70] (* Harvey P. Dale, Jul 03 2021 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^5)*(1-x^9)*(1-x^11)) + O(x^80)) \\ Jinyuan Wang, Mar 11 2020

Crossrefs

Sequence in context: A325002 A182594 A201593 * A055184 A366063 A238190

Adjacent sequences: A029284 A029285 A029286 * A029288 A029289 A029290

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved