A025801 - OEIS

A025801

Expansion of 1/((1-x^2)*(1-x^3)*(1-x^12)).

1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 4, 2, 4, 4, 4, 4, 6, 4, 6, 6, 6, 6, 9, 6, 9, 9, 9, 9, 12, 9, 12, 12, 12, 12, 16, 12, 16, 16, 16, 16, 20, 16, 20, 20, 20, 20, 25, 20, 25, 25, 25, 25, 30, 25, 30, 30, 30, 30, 36, 30, 36, 36, 36, 36, 42, 36, 42, 42, 42, 42, 49, 42

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,7

COMMENTS

Number of partitions of n into parts 2, 3, and 12. - Hoang Xuan Thanh, Aug 26 2025

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

FORMULA

a(n) = floor((n^2 + n*(17+3*(-1)^n) + 120 + 4*(n+6)*(((n+2) mod 3)-1))/144). - Hoang Xuan Thanh, Aug 26 2025

MATHEMATICA

CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^12)), {x, 0, 80}], x] (* or *) LinearRecurrence[{0, 1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, -1, 0, 1}, {1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 4, 2, 4, 4, 4}, 80] (* Harvey P. Dale, Apr 30 2018 *)

PROG

(PARI) Vec(1/((1-x^2)*(1-x^3)*(1-x^12)) + O(x^75)) \\ Jinyuan Wang, Feb 28 2020

(Magma)

R<x>:=PowerSeriesRing(Rationals(), 80);

Coefficients(R!( 1/((1-x^2)*(1-x^3)*(1-x^12)) )); // G. C. Greubel, Oct 29 2025

(SageMath)

def A025801_list(prec):

P.<x>= PowerSeriesRing(QQ, prec)

return P( 1/((1-x^2)*(1-x^3)*(1-x^12)) ).list()

print(A025801_list(81)) # G. C. Greubel, Oct 29 2025

CROSSREFS

Cf. A008615, A029142, A103221.