A025886 Expansion of 1/((1-x^5)*(1-x^7)*(1-x^12)).

1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 1, 0, 2, 0, 2, 1, 1, 2, 0, 3, 1, 2, 2, 1, 3, 1, 3, 2, 2, 3, 2, 4, 2, 3, 3, 3, 4, 3, 4, 3, 4, 4, 4, 5, 4, 5, 4, 5, 5, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 7, 7, 8, 7, 8, 8, 8, 9, 8, 9, 9, 9, 10, 9, 10

Offset

0,13

Comments

a(n) is the number of partitions of n into parts 5, 7, and 12. - Joerg Arndt, Nov 20 2022

Links

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

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

Formula

For n>23, a(n) = a(n-5) + a(n-7) - a(n-17) - a(n-19) + a(n-24). - Harvey P. Dale, Sep 28 2012

Mathematica

CoefficientList[Series[1/((1-x^5)(1-x^7)(1-x^12)), {x, 0, 80}], x] (* Harvey P. Dale, Sep 28 2012 *)
LinearRecurrence[{0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 1, 0, 2, 0, 2, 1, 1, 2, 0}, 80] (* Harvey P. Dale, Nov 02 2021 *)

Prog

(PARI) Vec(1/((1-x^5)*(1-x^7)*(1-x^12))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012
(Magma) R<x>:=PowerSeriesRing(Rationals(), 80); Coefficients(R!( 1/((1-x^5)*(1-x^7)*(1-x^12)) )); // G. C. Greubel, Nov 19 2022
(SageMath)
def A025886_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x^5)*(1-x^7)*(1-x^12)) ).list()
A025886_list(80) # G. C. Greubel, Nov 19 2022

Crossrefs

Cf. A025882, A025883, A025884, A025885.

Sequence in context: A284319 A281272 A147310 * A117355 A319571 A086966

Adjacent sequences: A025883 A025884 A025885 * A025887 A025888 A025889

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved