A017885 Expansion of 1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18).

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 17, 21, 26, 32, 39, 47, 57, 67, 79, 93, 110, 131, 157, 189, 228, 276, 332, 399, 478, 571, 681, 812, 969, 1158, 1387, 1662, 1994

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, 15, 16, 17 and 18. - 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 (0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1).

Crossrefs

Cf. A017877, A017878, A017879, A017880, A017881, A017882, A017883, A017884, 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-x^16-x^17-x^18))); // Vincenzo Librandi, Jul 01 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[9, 18]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jul 01 2013 *)

SageMath

def A017885_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/(1-x-x^9+x^(19)) ).list()
A017885_list(70) # 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) +a(n-16) +a(n-17) +a(n-18), for n>17. - Vincenzo Librandi, Jul 01 2013