OFFSET
0,18
COMMENTS
Number of compositions of n into parts p where 8 <= p <= 11. [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 (0,0,0,0,0,0,0,1,1,1,1).
FORMULA
G.f.: 1/(1-x^8-x^9-x^10-x^11).
a(n) = a(n-8) +a(n-9) +a(n-10) +a(n-11) for n>10. - Vincenzo Librandi, Jun 29 2013
MATHEMATICA
CoefficientList[Series[1 / (1 - Total[x^Range[8, 11]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 29 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1}, 60] (* Harvey P. Dale, Dec 31 2018 *)
PROG
(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^8-x^9-x^10-x^11))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]; [n le 11 select I[n] else Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11): n in [1..70]]; // Vincenzo Librandi, Jun 29 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved