OFFSET
0,12
COMMENTS
Number of compositions of n into parts p where 5 <= p <= 8. [Joerg Arndt, Jun 27 2013]
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,1,1,1).
FORMULA
a(a) = a(n-5) +a(n-6) +a(n-7) +a(n-8) for n>7. - Vincenzo Librandi, Jun 27 2013
MATHEMATICA
CoefficientList[Series[1 / (1 - Total[x^Range[5, 8]]), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 27 2013 *)
LinearRecurrence[{0, 0, 0, 0, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 1, 1, 1}, 60] (* Harvey P. Dale, Jan 18 2015 *)
PROG
(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^5-x^6-x^7-x^8))); /* or */ I:=[1, 0, 0, 0, 0, 1, 1, 1]; [n le 8 select I[n] else Self(n-5)+Self(n-6)+Self(n-7)+Self(n-8): n in [1..70]]; // Vincenzo Librandi, Jun 27 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved