A017889 - OEIS

A017889

Expansion of 1/(1-x^10-x^11-x^12-x^13).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 3, 2, 1, 0, 0, 0, 1, 3, 6, 10, 12, 12, 10, 6, 3, 1, 1, 4, 10, 20, 31, 40, 44, 40, 31, 20, 11, 9, 16, 35, 65, 101, 135, 155, 155, 135, 102, 71, 56, 71, 125

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,22

COMMENTS

Number of compositions (ordered partitions) of n into parts 10, 11, 12 and 13. - 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 (0,0,0,0,0,0,0,0,0,1,1,1,1).

FORMULA

a(n) = a(n-10) +a(n-11) +a(n-12) +a(n-13) for n>12. - Vincenzo Librandi, Jul 01 2013

MATHEMATICA

CoefficientList[Series[1 / (1 - Total[x^Range[10, 13]]), {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-x^13))); // Vincenzo Librandi, Jul 01 2013

(SageMath)

def A017889_list(prec):

P.<x> = PowerSeriesRing(ZZ, prec)

return P( (1-x)/(1-x-x^10+x^(14)) ).list()

A017889_list(80) # G. C. Greubel, Sep 25 2024

CROSSREFS

Cf. A017887, A017888, A017890, A017891, A017892, A017893, A017894, A017895, A017896.

Sequence in context: A299730 A141470 A141331 * A017879 A179764 A266313

Adjacent sequences: A017886 A017887 A017888 * A017890 A017891 A017892

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved