A025881 Expansion of 1/((1-x^5)*(1-x^6)*(1-x^12)).

1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 2, 0, 0, 1, 1, 2, 2, 0, 1, 1, 2, 2, 3, 1, 1, 2, 2, 3, 4, 1, 2, 2, 3, 4, 5, 2, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 10, 5, 6, 7, 8, 10, 11, 6, 7, 8, 10, 11, 13, 7, 8, 10, 11, 13, 14, 8, 10, 11, 13

Offset

0,13

Comments

a(n) is the number of partitions of n into parts 5, 6, and 12. - Joerg Arndt, Nov 19 2022

Links

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

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

Formula

a(n) = floor((n^2 - 2*n + 145)/720 + (n+12)*((n+5) mod 6)/72). - Hoang Xuan Thanh, Sep 16 2025

Mathematica

CoefficientList[Series[1/((1-x^5)(1-x^6)(1-x^12)), {x, 0, 80}], x] (* Harvey P. Dale, Nov 26 2020 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Rationals(), 90); Coefficients(R!( 1/((1-x^5)*(1-x^6)*(1-x^12)) )); // G. C. Greubel, Nov 18 2022
(SageMath)
def A025881_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x^5)*(1-x^6)*(1-x^12)) ).list()
A025881_list(90) # G. C. Greubel, Nov 18 2022
(PARI) a(n) = (n^2-2*n+145 + 10*(n+12)*((n+5)%6))\720 \\ Hoang Xuan Thanh, Sep 16 2025

Crossrefs

Cf. A025876, A025877, A025878, A025879, A025880.

Sequence in context: A035144 A157045 A035208 * A039804 A277537 A323179

Adjacent sequences: A025878 A025879 A025880 * A025882 A025883 A025884

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved