A017886 Expansion of 1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18-x^19).

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 11, 14, 16, 19, 23, 28, 34, 41, 49, 59, 72, 86, 102, 122, 146, 175, 210, 252, 303, 366, 441, 529, 635, 762, 914, 1096, 1314, 1576, 1893, 2275

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of compositions of n into parts 9, 10, 11, ..., 19. - Joerg Arndt, Oct 12 2014

Links

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

Crossrefs

Cf. A017877, A017878, A017879, A017880, A017881, A017882, A017883, A017884, A017885, A017887.

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-x^19))); // Vincenzo Librandi, Jul 01 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[9, 19]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jul 01 2013 *)

SageMath

def A017886_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/(1-x-x^9+x^(20)) ).list()
A017886_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) +a(n-19) for n>18. - Vincenzo Librandi, Jul 01 2013

a(n) = a(n-1) +a(n-9) -a(n-20) for n>19. - Tani Akinari, Sep 29 2014