A029290 Expansion of 1/((1-x^3)*(1-x^5)*(1-x^10)*(1-x^12)).

1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 2, 1, 2, 2, 1, 4, 2, 2, 4, 2, 5, 4, 4, 5, 5, 7, 5, 7, 7, 6, 11, 7, 9, 11, 9, 13, 12, 12, 13, 14, 17, 14, 18, 17, 17, 23, 19, 21, 24, 22, 27, 26, 27, 28, 30, 33, 31, 35, 35, 35, 43, 38, 41, 45, 43

Offset

0,11

Comments

Number of partitions of n into parts 3, 5, 10, and 12. - Vincenzo Librandi, Jun 04 2014

Links

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

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

Formula

a(n) = floor((n^3+45*n^2+312*n+1735)/10800 - (n mod 2)*n/240 + ((2*n^2+1) mod 3)*(n+12)/36 + ((2*n^2+3) mod 5)*n/50 + ((4*n^2+3*n+4) mod 5)/5). - Hoang Xuan Thanh, Apr 02 2026

Mathematica

CoefficientList[Series[1/((1 - x^3) (1 - x^5) (1 - x^10) (1 - x^12)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 04 2014 *)
LinearRecurrence[{0, 0, 1, 0, 1, 0, 0, -1, 0, 1, 0, 1, -1, 0, -2, 0, -1, 1, 0, 1, 0, -1, 0, 0, 1, 0, 1, 0, 0, -1}, {1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 2, 1, 2, 2, 1, 4, 2, 2, 4, 2, 5, 4, 4, 5, 5, 7, 5, 7, 7, 6}, 70] (* Harvey P. Dale, Oct 02 2021 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^5)*(1-x^10)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 11 2020

Crossrefs

Sequence in context: A105272 A060438 A106190 * A115311 A035436 A242210

Adjacent sequences: A029287 A029288 A029289 * A029291 A029292 A029293

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved