A017890 Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 1, 3, 6, 10, 15, 18, 19, 18, 15, 10, 7, 7, 11, 20, 35, 52, 68, 80, 85, 80, 69, 57, 50, 55, 80, 125, 186, 255, 320, 365, 382, 371, 341, 311, 311, 367, 496, 701, 966, 1251, 1508, 1693, 1779, 1770, 1716, 1701, 1826

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

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

Crossrefs

Cf. A017887.

Programs

Magma

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

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[10, 14]]), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 01 2013 *)

SageMath

def A017890_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/(1-x-x^10+x^15) ).list()
A017890_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) for n>13. - Vincenzo Librandi, Jul 01 2013