A017879 Expansion of 1/(1-x^9-x^10-x^11-x^12).

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 2, 3, 4, 3, 2, 1, 0, 0, 1, 3, 6, 10, 12, 12, 10, 6, 3, 2, 4, 10, 20, 31, 40, 44, 40, 31, 21, 15, 19, 36, 65, 101, 135, 155, 155, 136, 107, 86, 91, 135, 221, 337, 456, 546

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of compositions (ordered partitions) of n into parts 9, 10, 11 and 12. - 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 (0,0,0,0,0,0,0,0,1,1,1,1).

Crossrefs

Cf. A017877, A017878, 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-x^12))); // Vincenzo Librandi, Jul 01 2013

Mathematica

CoefficientList[Series[1/(1-x^9 -x^10 -x^11 -x^12), {x,0,70}], x] (* or *) LinearRecurrence[{0,0,0,0,0,0,0,0,1,1,1,1}, {1,0,0,0,0,0,0,0,0,1,1,1}, 70] (* Harvey P. Dale, Apr 29 2013 *)
CoefficientList[Series[1/(1 - Total[x^Range[9, 12]]), {x,0,70}], x] (* Vincenzo Librandi, Jul 01 2013 *)

SageMath

def A017879_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/(1-x-x^9+x^(13)) ).list()
A017879_list(85) # G. C. Greubel, Sep 25 2024

Formula

a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=0, a(7)=0, a(8)=0, a(9)=1, a(10)=1, a(11)=1; for n>11, a(n) = a(n-9)+a(n-10)+a(n-11)+a(n-12). - Harvey P. Dale, Apr 29 2013