A017889 Expansion of 1/(1-x^10-x^11-x^12-x^13).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 3, 2, 1, 0, 0, 0, 1, 3, 6, 10, 12, 12, 10, 6, 3, 1, 1, 4, 10, 20, 31, 40, 44, 40, 31, 20, 11, 9, 16, 35, 65, 101, 135, 155, 155, 135, 102, 71, 56, 71, 125

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of compositions (ordered partitions) of n into parts 10, 11, 12 and 13. - Ilya Gutkovskiy, May 27 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1,1,1,1).

Crossrefs

Cf. A017887, A017888, A017890, A017891, A017892, A017893, A017894, A017895, A017896.

Programs

Magma

m:=80; R:=PowerSeriesRing(Integers(), m);
Coefficients(R!(1/(1-x^10-x^11-x^12-x^13))); // Vincenzo Librandi, Jul 01 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[10, 13]]), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 01 2013 *)

SageMath

def A017889_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/(1-x-x^10+x^(14)) ).list()
A017889_list(80) # G. C. Greubel, Sep 25 2024

Formula

a(n) = a(n-10) +a(n-11) +a(n-12) +a(n-13) for n>12. - Vincenzo Librandi, Jul 01 2013