A017877 Expansion of 1/(1 - x^9 - x^10).

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 0, 1, 6, 15, 20, 15, 6, 1, 0, 0, 1, 7, 21, 35, 35, 21, 7, 1, 0, 1, 8, 28, 56

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of compositions (ordered partitions) of n into parts 9 and 10. - 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).

Crossrefs

Column k=9 of A306713.

Cf. A017876, A017878, A017879, A017880, A017881, A017882, A017883, A017884, A017885, A017886.

Programs

Magma

m:=80; R:=PowerSeriesRing(Integers(), m);
Coefficients(R!(1/(1-x^9-x^10))); // Vincenzo Librandi, Jul 01 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[9, 10]]), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 01 2013 *)

SageMath

def A017877_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-x^9-x^(10)) ).list()
A017877_list(85) # G. C. Greubel, Sep 25 2024

Formula

a(n) = a(n-9) + a(n-10) for n > 9. - Vincenzo Librandi, Jul 01 2013

a(n) = Sum_{k=0..floor(n/9)} binomial(k,n-9*k). - Seiichi Manyama, Oct 01 2024