OFFSET
0,9
COMMENTS
Number of compositions (ordered partitions) of n into parts 4, 5, 6, 7 and 8. - Ilya Gutkovskiy, May 25 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,1,1,1,1).
FORMULA
a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=1, a(5)=1, a(6)=1, a(7)=1; for n>7, a(n) = a(n-4)+a(n-5)+a(n-6)+a(n-7)+a(n-8). [Harvey P. Dale, Aug 05 2011]
MATHEMATICA
CoefficientList[Series[1/(1 - Total[x^Range[4, 8]]), {x, 0, 50}], x] (* or *) LinearRecurrence[{0, 0, 0, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 1, 1, 1, 1}, 50] (* Harvey P. Dale, Aug 05 2011 *)
PROG
(Magma) I:=[1, 0, 0, 0, 1, 1, 1, 1]; [n le 8 select I[n] else Self(n-4)+Self(n-5)+Self(n-6)+Self(n-7)+Self(n-8): n in [1..50]]; /* or */ m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^4-x^5-x^6-x^7-x^8))); // Vincenzo Librandi, Jun 27 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved