A017894 Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 8, 9, 11, 14, 18, 23, 29, 36, 45, 52, 58, 64, 71, 80, 92, 108, 129, 156, 193, 237, 286, 339, 396, 458, 527, 606, 699, 810, 951, 1130, 1352, 1620, 1936, 2302, 2721, 3198, 3741, 4358, 5072, 5916, 6929, 8153, 9631

Offset

0,22

Comments

Number of compositions (ordered partitions) of n into parts 10, 11, 12, 13, 14, 15, 16, 17 and 18. - 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 (0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1).

Formula

a(n) = a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) +Self(n-16) +a(n-17) +a(n-18), for n>17. - Vincenzo Librandi, Jul 01 2013

Maple

a:= n-> (Matrix(18, (i, j)-> if (i=j-1) or (j=1 and i in [$10..18]) then 1 else 0 fi)^n)[1, 1]: seq(a(n), n=0..80);  # Alois P. Heinz, Jul 01 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[10, 18]]), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 01 2013 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 80);
Coefficients(R!(1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18))); // Vincenzo Librandi, Jul 01 2013
(SageMath)
def A017894_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/(1-x-x^10+x^19) ).list()
A017894_list(80) # G. C. Greubel, Nov 06 2024

Crossrefs

Cf. A017887.

Sequence in context: A287794 A179987 A073796 * A291571 A341191 A232897

Adjacent sequences: A017891 A017892 A017893 * A017895 A017896 A017897

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved