A029059 Expansion of 1/((1-x)*(1-x^3)*(1-x^9)*(1-x^11)).

1, 1, 1, 2, 2, 2, 3, 3, 3, 5, 5, 6, 8, 8, 9, 11, 11, 12, 15, 15, 17, 20, 21, 23, 26, 27, 29, 33, 34, 37, 41, 43, 46, 51, 53, 56, 62, 64, 68, 74, 77, 81, 88, 91, 96, 104, 107, 113, 121, 125, 131, 140, 144, 151, 161, 166

Offset

0,4

Comments

Number of partitions of n into parts 1, 3, 9 and 11. - Ilya Gutkovskiy, May 16 2017

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = floor((n^3+36*n^2+357*n+1782)/1782 + (n/27)*[(n mod 3)=0] + (3/11)*([(n mod 11) in {1,3}] - [(n mod 11) in {6,8}])). - Hoang Xuan Thanh, Jul 09 2025

Mathematica

CoefficientList[Series[1/((1 - x)*(1 - x^3)*(1 - x^9)*(1 - x^11)), {x, 0, 50}], x] (* G. C. Greubel, May 17 2017 *)
LinearRecurrence[{1, 0, 1, -1, 0, 0, 0, 0, 1, -1, 1, -2, 1, -1, 1, 0, 0, 0, 0, -1, 1, 0, 1, -1}, {1, 1, 1, 2, 2, 2, 3, 3, 3, 5, 5, 6, 8, 8, 9, 11, 11, 12, 15, 15, 17, 20, 21, 23}, 80] (* Harvey P. Dale, Apr 21 2019 *)

Prog

(PARI) x='x+O('x^50); Vec(1/((1-x)*(1-x^3)*(1-x^9)*(1-x^11))) \\ G. C. Greubel, May 17 2017

Crossrefs

Sequence in context: A261736 A328796 A247049 * A035449 A161555 A029058

Adjacent sequences: A029056 A029057 A029058 * A029060 A029061 A029062

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved