A029038 Expansion of 1/((1-x)*(1-x^3)*(1-x^4)*(1-x^12)).

1, 1, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 17, 20, 21, 24, 27, 30, 33, 36, 39, 45, 48, 51, 57, 63, 66, 72, 78, 84, 90, 96, 102, 112, 118, 124, 134, 144, 150, 160, 170, 180, 190, 200, 210, 225, 235, 245, 260, 275

Offset

0,4

Comments

Number of partitions of n into parts 1, 3, 4 and 12. - Ilya Gutkovskiy, May 14 2017

Links

Table of n, a(n) for n=0..52.

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

Formula

a(n) = floor((n^3 + 30*n^2 + 252*n + 846)/864 - (n/36)*[(n mod 3)=2] + ((n+2)/96)*((n mod 4)-2)^2). - Hoang Xuan Thanh, Jul 30 2025

Mathematica

CoefficientList[Series[1/((1 - x)*(1 - x^3)*(1 - x^4)*(1 - x^12)), {x, 0, 52}], x] (* Hoang Xuan Thanh, Jul 30 2025 *)

Prog

(PARI) Vec(1/((1 - x)*(1 - x^3)*(1 - x^4)*(1 - x^12))+ O(x^53)) \\ Hoang Xuan Thanh, Jul 30 2025
(PARI) a(n) = (n^3 + 30*n^2 + 252*n + 846 + 9*(n+2)*((n%4)-2)^2 - 12*n*((n%3)*((n%3)-1)))\ 864 \\ Hoang Xuan Thanh, Aug 11 2025

Crossrefs

Sequence in context: A025767 A091848 A017886 * A011877 A029064 A029037

Adjacent sequences: A029035 A029036 A029037 * A029039 A029040 A029041

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved