A017887 Expansion of 1/(1 - x^10 - x^11).

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of compositions (ordered partitions) of n into parts 10 and 11. - 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).

Crossrefs

Column k=10 of A306713.

Cf. A017886, A017888, A017889, A017890, A017891, A017892, A017893, A017894, A017895, A017896.

Programs

Magma

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

Magma

I:=[1,0,0,0,0,0,0,0,0,0,1]; [n le 11 select I[n] else Self(n-10)+Self(n-11): n in [1..80]]; // Vincenzo Librandi, Jul 01 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[10, 11]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jul 01 2013 *)
LinearRecurrence[{0,0,0,0,0,0,0,0,0,1,1},{1,0,0,0,0,0,0,0,0,0,1},100] (* Harvey P. Dale, Feb 04 2015 *)

SageMath

def A017887_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-x^10-x^(11)) ).list()
A017887_list(100) # G. C. Greubel, Sep 25 2024

Formula

a(n) = a(n-10) + a(n-11) for n > 10. - Vincenzo Librandi, Jul 01 2013

a(n) = Sum_{k=0..floor(n/10)} binomial(k,n-10*k). - Seiichi Manyama, Oct 01 2024