A029236 Expansion of 1/((1-x^2)*(1-x^8)*(1-x^9)*(1-x^10)).

1, 0, 1, 0, 1, 0, 1, 0, 2, 1, 3, 1, 3, 1, 3, 1, 4, 2, 6, 3, 7, 3, 7, 3, 8, 4, 10, 6, 12, 7, 13, 7, 14, 8, 16, 10, 19, 12, 21, 13, 23, 14, 25, 16, 28, 19, 31, 21, 34, 23, 37, 25, 40, 28, 44, 31, 48, 34, 52, 37, 56, 40, 60, 44, 65, 48, 70, 52, 75, 56, 80, 60, 86

Offset

0,9

Comments

Number of partitions of n into parts 2, 8, 9, and 10. - Vincenzo Librandi, Jun 03 2014

Links

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

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

Formula

a(n) = floor((n^3+57*n^2+960*n+8432)/8640 - (n mod 2)*(n^2+29*n+176)/320 + ((n+2) mod 3)/27 + (2*((n+9) mod 10) - ((n+5) mod 10) - ((n+3) mod 10))/50). - Hoang Xuan Thanh, Jun 15 2026

Mathematica

CoefficientList[Series[1/((1 - x^2) (1 - x^8) (1 - x^9) (1 - x^10)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 03 2014 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^8)*(1-x^9)*(1-x^10)) + O(x^80)) \\ Jinyuan Wang, Mar 15 2020

Crossrefs

Sequence in context: A382936 A378445 A029242 * A152188 A239930 A226859

Adjacent sequences: A029233 A029234 A029235 * A029237 A029238 A029239

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved