A017888 Expansion of 1/(1 - x^10 - x^11 - x^12).

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

Offset

0,22

Comments

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

Formula

a(n) = a(n-10) + a(n-11) + a(n-12), for n > 11. - Vincenzo Librandi, Jul 01 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[10, 12]]), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 01 2013 *)

Prog

(Magma)
m:=80; R<x>:=PowerSeriesRing(Integers(), m);
Coefficients(R!(1/(1-x^10-x^11-x^12))); // Vincenzo Librandi, Jul 01 2013
(PARI)
my(x='x+O('x^80)); Vec(1/(1-x^10-x^11-x^12)) \\ Altug Alkan, Oct 04 2018
(SageMath)
def A017888_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/(1-x-x^10+x^(13)) ).list()
A017888_list(80) # G. C. Greubel, Sep 25 2024

Crossrefs

Cf. A017887, A017889, A017890, A017891, A017892, A017893, A017894, A017895, A017896.

Sequence in context: A332742 A202815 A049336 * A017878 A301572 A017868

Adjacent sequences: A017885 A017886 A017887 * A017889 A017890 A017891

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved