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

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..70);  # Alois P. Heinz, Jul 01 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[10, 18]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jul 01 2013 *)

Prog

(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]; [n le 18 select I[n] else Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13)+Self(n-14)+Self(n-15)+Self(n-16)+Self(n-17)+Self(n-18): n in [1..70]]; // Vincenzo Librandi, Jul 01 2013

Crossrefs

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