A017882 Expansion of 1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15).

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 5, 6, 8, 11, 15, 21, 28, 33, 36, 38, 40, 43, 48, 56, 71, 94, 122, 152, 182, 211, 239, 266, 294, 332, 390, 474, 586, 725, 888, 1071, 1266, 1466

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of compositions (ordered partitions) of n into parts 9, 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 (0,0,0,0,0,0,0,0,1,1,1,1,1,1,1).

Crossrefs

Cf. A017877, A017878, A017879, A017880, A017881, A017883, A017884, A017885, A017886.

Programs

Magma

m:=70; R:=PowerSeriesRing(Integers(), m);
Coefficients(R!(1/(1-x^9-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[9, 15]]),{x, 0, 80}], x] (* Vincenzo Librandi, Jul 01 2013 *)

SageMath

def A017882_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/(1-x-x^9+x^(16)) ).list()
A017882_list(80) # G. C. Greubel, Sep 25 2024

Formula

a(n) = a(n-9) +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