A017891 Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 2, 3, 6, 10, 15, 21, 25, 27, 27, 25, 22, 19, 20, 26, 38, 57, 80, 104, 125, 140, 147, 145, 140, 139, 150, 182, 240, 325, 430, 544, 653, 741, 801, 836, 861, 903, 996, 1176, 1466, 1871, 2374, 2933, 3494, 4005, 4436

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of compositions (ordered partitions) of n into parts 10, 11, 12, 13, 14 and 15. - 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 (0,0,0,0,0,0,0,0,0,1,1,1,1,1,1).

Crossrefs

Cf. A017887.

Programs

Magma

R:=PowerSeriesRing(Integers(), 80);
Coefficients(R!(1/(1-x^10-x^11-x^12-x^13-x^14-x^15))); // Vincenzo Librandi, Jul 01 2013

Mathematica

CoefficientList[Series[1/(1 - Total[x^Range[10, 15]]), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 01 2013 *)

SageMath

def A017891_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/(1-x-x^10+x^16) ).list()
A017891_list(80) # G. C. Greubel, Nov 06 2024

Formula

a(n) = a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) for n>14. - Vincenzo Librandi, Jul 01 2013