A017878 Expansion of 1/(1-x^9-x^10-x^11).

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 3, 2, 1, 0, 0, 0, 0, 1, 3, 6, 7, 6, 3, 1, 0, 0, 1, 4, 10, 16, 19, 16, 10, 4, 1, 1, 5, 15, 30, 45, 51, 45, 30, 15, 6, 7, 21, 50, 90, 126, 141, 126, 90, 51, 28, 34, 78, 161

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of compositions (ordered partitions) of n into parts 9, 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 (0,0,0,0,0,0,0,0,1,1,1).

Crossrefs

Cf. A017877, A017879, A017880, A017881, A017882, A017883, A017884, A017885, A017886.

Programs

Magma

m:=70; R:=PowerSeriesRing(Integers(), m);
Coefficients(R!(1/(1-x^9-x^10-x^11))); // Vincenzo Librandi, Jul 01 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[9, 11]]), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 01 2013 *)
LinearRecurrence[{0,0,0,0,0,0,0,0,1,1,1},{1,0,0,0,0,0,0,0,0,1,1},70] (* Harvey P. Dale, May 25 2023 *)

SageMath

def A017878_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/(1-x-x^9+x^(12)) ).list()
A017878_list(80) # G. C. Greubel, Sep 25 2024

Formula

a(n) = a(n-9) +a(n-10) +a(n-11) for n>10. - Vincenzo Librandi, Jul 01 2013