A029165 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^9)*(1-x^10)).

1, 0, 1, 1, 1, 1, 2, 1, 2, 3, 3, 3, 5, 4, 5, 6, 6, 6, 9, 8, 10, 11, 12, 12, 15, 14, 16, 18, 19, 20, 24, 23, 26, 28, 29, 30, 35, 34, 38, 41, 43, 44, 50, 49, 53, 57, 59, 61, 68, 68, 73, 77, 80, 82, 90, 90, 96, 101, 105, 108, 117, 117, 124, 130, 134, 138, 148, 149

Offset

0,7

Comments

Number of partitions of n into parts 2, 3, 9, and 10. - Hoang Xuan Thanh, Oct 06 2025

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..5000

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

Formula

a(n) = floor((n^3+36*n^2+504*n+3320)/3240 - (n+2)*(n mod 2)/40 - (n+8)*(n^2 mod 3)/27). - Hoang Xuan Thanh, Oct 06 2025

Mathematica

CoefficientList[Series[1/((1 - x^2) (1 - x^3) (1 - x^9) (1 - x^10)), {x, 0, 100}], x] (* Vincenzo Librandi, Jan 22 2017 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^3)*(1-x^9)*(1-x^10)) + O(x^90)) \\ Michel Marcus, Jan 22 2017
(Magma) m:=100; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! 1/((1-x^2)*(1-x^3)*(1-x^9)*(1-x^10))); // Vincenzo Librandi, Jan 22 2017

Crossrefs

Sequence in context: A186519 A241091 A137719 * A035431 A008681 A362559

Adjacent sequences: A029162 A029163 A029164 * A029166 A029167 A029168

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Jason Yuen, Oct 07 2025.

Status

approved