A029266 Expansion of 1/((1-x^3)*(1-x^4)*(1-x^9)*(1-x^10)).

1, 0, 0, 1, 1, 0, 1, 1, 1, 2, 2, 1, 3, 3, 2, 3, 4, 3, 5, 5, 5, 6, 7, 6, 8, 8, 8, 10, 11, 10, 13, 13, 13, 15, 16, 15, 19, 19, 19, 22, 24, 22, 26, 27, 27, 30, 32, 31, 36, 37, 37, 40, 43, 42, 47, 48, 49, 53, 56, 55, 61, 62, 63, 68, 71, 70, 77, 79, 80, 85, 89, 88, 96

Offset

0,10

Comments

Number of partitions of n into parts 3, 4, 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 (0,0,1,1,0,0,-1,0,1,1,0,-1,-2,-1,0,1,1,0,-1,0,0,1,1,0,0,-1).

Formula

a(n) = floor((n^3+39*n^2+576*n+6480)/6480 - (n mod 2)*n/80 - ((2*n^2+n) mod 3)*n/27 - (n mod 3)/3 + ([(n mod 9)=4] - [(n mod 9)=6])/3). - Hoang Xuan Thanh, Mar 25 2026

Mathematica

CoefficientList[Series[1/((1 - x^3) (1 - x^4) (1-x^9) (1 - x^10)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 03 2014 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^4)*(1-x^9)*(1-x^10)) + O(x^75)) \\ Hoang Xuan Thanh, Mar 25 2026

Crossrefs

Sequence in context: A274515 A362500 A291564 * A325035 A348331 A035387

Adjacent sequences: A029263 A029264 A029265 * A029267 A029268 A029269

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved