A017867 Expansion of 1/(1-x^8-x^9).

1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 1, 6, 15, 20, 15, 6, 1, 0, 1, 7, 21, 35, 35, 21, 7, 1, 1, 8, 28, 56, 70, 56, 28, 8, 2, 9

Offset

0,18

Comments

Number of compositions of n into parts 8 and 9. [Joerg Arndt, Jun 29 2013]

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).

Formula

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

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[8, 9]]), {x, 0, 80}], x] (* Vincenzo Librandi, Jun 28 2013 *)

Prog

(Magma) m:=80; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^8-x^9))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 0, 1]; [n le 9 select I[n] else Self(n-8)+Self(n-9): n in [1..80]]; // Vincenzo Librandi, Jun 28 2013
(PARI) x='x+O('x^66); Vec(1/(1-x^8-x^9)) \\ Altug Alkan, Oct 07 2018

Crossrefs

Sequence in context: A284093 A284095 A279593 * A127843 A350750 A154234

Adjacent sequences: A017864 A017865 A017866 * A017868 A017869 A017870

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved