A029044 Expansion of 1/((1-x)*(1-x^3)*(1-x^5)*(1-x^12)).

1, 1, 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 10, 11, 12, 15, 16, 18, 21, 22, 25, 28, 30, 33, 37, 40, 43, 48, 51, 55, 61, 64, 69, 75, 79, 85, 92, 97, 103, 111, 117, 124, 133, 139, 147, 157, 164, 173, 184, 192, 202, 214, 223, 234

Offset

0,4

Comments

Number of partitions of n into parts 1, 3, 5 and 12. - Ilya Gutkovskiy, May 14 2017

Links

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

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

Formula

a(n) = floor((2*n^3 + 63*n^2 + 552*n + 60*n*[(n mod 3)=0] + 2295)/2160) + [(n mod 60)=30]. - Hoang Xuan Thanh, Jul 02 2025

Mathematica

CoefficientList[Series[1/((1 - x) (1 - x^3) (1 - x^5) (1 - x^12)), {x, 0, 60}], x] (* Vincenzo Librandi, Jun 26 2014 *)
LinearRecurrence[{1, 0, 1, -1, 1, -1, 0, -1, 1, 0, 0, 1, -1, 0, -1, 1, -1, 1, 0, 1, -1}, {1, 1, 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 10, 11, 12, 15, 16, 18, 21, 22, 25}, 61] (* Harvey P. Dale, Nov 09 2016 *)

Prog

(PARI) a(n)=floor((2*n^3+63*n^2+552*n+2155+10*(n%3<1)*(6*n+59+27*(-1)^(n\3)))/2160) \\ Tani Akinari, Jun 25 2014

Crossrefs

Sequence in context: A027582 A259198 A011880 * A029043 A296371 A337601

Adjacent sequences: A029041 A029042 A029043 * A029045 A029046 A029047

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved