A017868 Expansion of 1/(1-x^8-x^9-x^10).

1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 2, 3, 2, 1, 0, 0, 0, 1, 3, 6, 7, 6, 3, 1, 0, 1, 4, 10, 16, 19, 16, 10, 4, 2, 5, 15, 30, 45, 51, 45, 30, 16, 11, 22, 50, 90, 126, 141, 126, 91, 57, 49, 83, 162, 266, 357, 393, 358

Offset

0,18

Comments

Number of compositions (ordered partitions) of n into parts 8, 9 and 10. - Ilya Gutkovskiy, May 26 2017

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1,1,1).

Formula

a(n) = a(n-8) +a(n-9) +a(n-10) for n>9. - Vincenzo Librandi, Jun 28 2013

Mathematica

CoefficientList[Series[1/(1 - Total[x^Range[8, 10]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 28 2013 *)

Prog

(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^8-x^9-x^10))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 0, 1, 1]; [n le 10 select I[n] else Self(n-8)+Self(n-9)+Self(n-10): n in [1..70]]; // Vincenzo Librandi, Jun 28 2013

Crossrefs

Sequence in context: A017888 A017878 A301572 * A353158 A334476 A319573

Adjacent sequences: A017865 A017866 A017867 * A017869 A017870 A017871

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved