A017883 Expansion of 1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16).

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 7, 8, 10, 13, 17, 22, 28, 36, 42, 47, 52, 58, 66, 77, 92, 112, 141, 176, 215, 257, 302, 351, 406, 470, 546, 645, 774, 937, 1136, 1372, 1646

Offset

0,20

Comments

Number of compositions (ordered partitions) of n into parts 9, 10, 11, 12, 13, 14, 15 and 16. - 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 (0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1).

Formula

a(n) = a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) +a(n-16) for n>15. - Vincenzo Librandi, Jul 01 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[9, 16]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jul 01 2013 *)

Prog

(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]; [n le 16 select I[n] else Self(n-9)+Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13)+Self(n-14)+Self(n-15)+Self(n-16): n in [1..70]]; // Vincenzo Librandi, Jul 01 2013

Crossrefs

Sequence in context: A287793 A073795 A017893 * A269364 A309384 A245353

Adjacent sequences: A017880 A017881 A017882 * A017884 A017885 A017886

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved