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

0,22

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).

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

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 *)

Prog

(Magma) m:=80; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^10-x^11))); /* or */ 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
(SageMath)
def A017887_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-x^10-x^(11)) ).list()
A017887_list(100) # G. C. Greubel, Sep 25 2024

Crossrefs

Column k=10 of A306713.

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

Sequence in context: A067150 A356995 A289922 * A289923 A289921 A219482

Adjacent sequences: A017884 A017885 A017886 * A017888 A017889 A017890

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved