A029250 Expansion of 1/((1-x^3)(1-x^4)(1-x^5)(1-x^12)).

1, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 3, 3, 5, 5, 5, 6, 6, 8, 8, 8, 9, 12, 11, 11, 14, 15, 15, 17, 17, 20, 21, 21, 23, 27, 26, 27, 31, 33, 33, 36, 37, 41, 43, 43, 46, 52, 51, 53, 58, 61, 62, 66, 68, 73, 76, 77, 81, 89, 88

Offset

0,9

Comments

Number of partitions of n into parts 3, 4, 5, and 12. - 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 (0,0,1,1,1,0,-1,-1,-1,0,0,2,0,0,-1,-1,-1,0,1,1,1,0,0,-1).

Formula

G.f.: 1/((1-x^3)*(1-x^4)*(1-x^5)*(1-x^12)).

a(n) = a(n-3)+a(n-4)+a(n-5)-a(n-7)-a(n-8)-a(n-9)+2*a(n-12)-a(n-15)-a(n-16)-a(n-17)+a(n-19)+a(n-20)+a(n-21)-a(n-24). - Wesley Ivan Hurt, Aug 19 2022

Mathematica

CoefficientList[Series[1/((1 - x^3) (1 - x^4) (1 - x^5) (1 - x^12)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 03 2014 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^4)*(1-x^5)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 12 2020

Crossrefs

Sequence in context: A023159 A098983 A097576 * A341584 A110884 A303637

Adjacent sequences: A029247 A029248 A029249 * A029251 A029252 A029253

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved