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
a(n) = Sum_{k=0..floor(n/8)} binomial(k,n-8*k). - Seiichi Manyama, Oct 01 2024
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved