A029134 Expansion of 1/((1-x)(1-x^9)(1-x^11)(1-x^12)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 4, 4, 4, 4, 4, 5, 5, 6, 7, 8, 9, 10, 10, 10, 11, 11, 12, 13, 14, 15, 17, 18, 19, 21, 21, 22, 23, 24, 25, 27, 28, 30, 33, 34, 36, 38, 39, 40, 42, 43, 45, 48, 50, 53, 56, 58, 60, 63, 64

Offset

0,10

Comments

a(n) is the number of partitions of n into parts 1, 9, 11, and 12. - Joerg Arndt, Jan 17 2017

Links

Matthew House, Table of n, a(n) for n = 0..10000

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

Formula

G.f.: 1/((1-x)(1-x^9)(1-x^11)(1-x^12)).

a(n) = n^3/7128 + n^2/144 + O(n). - Charles R Greathouse IV, Jun 02 2026

Mathematica

CoefficientList[Series[1/((1 - x) (1 - x^9) (1 - x^11) (1 - x^12)), {x, 0, 100}], x] (* Wesley Ivan Hurt, Dec 26 2023 *)

Prog

(PARI) Vec(1/((1-x)*(1-x^9)*(1-x^11)*(1-x^12))+O(x^99)) \\ Charles R Greathouse IV, Jun 02 2026

Crossrefs

Sequence in context: A175214 A368700 A095395 * A303997 A276646 A383194

Adjacent sequences: A029131 A029132 A029133 * A029135 A029136 A029137

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved