A025880 Expansion of 1/((1-x^5)*(1-x^6)*(1-x^11)).

1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 1, 0, 0, 1, 2, 2, 1, 0, 1, 2, 3, 2, 1, 1, 2, 3, 3, 2, 2, 2, 3, 4, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 10, 9, 9, 9, 10, 11, 11, 10, 10, 11, 12

Offset

0,12

Comments

a(n) is the number of partitions of n into parts 5, 6, and 11. - 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 (0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,1).

Formula

a(n) = a(n-5) + a(n-6) + a(n-16) - a(n-17) + a(n-22) for n >= 22. - Harvey P. Dale, Jul 08 2014

Mathematica

CoefficientList[Series[1/((1-x^5)(1-x^6)(1-x^11)), {x, 0, 100}], x] (* or *)
LinearRecurrence[{0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 1, 0, 0, 1, 2, 2, 1, 0, 1, 2}, 100] (* Harvey P. Dale, Jul 08 2014 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Rationals(), 90); Coefficients(R!( 1/((1-x^5)*(1-x^6)*(1-x^11)) )); // G. C. Greubel, Nov 18 2022
(SageMath)
def A025880_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x^5)*(1-x^6)*(1-x^11)) ).list()
A025880_list(90) # G. C. Greubel, Nov 18 2022

Crossrefs

Cf. A025876, A025877, A025878, A025879, A025881.

Sequence in context: A004197 A261684 A048571 * A058755 A128519 A303979

Adjacent sequences: A025877 A025878 A025879 * A025881 A025882 A025883

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved