OFFSET
0,11
COMMENTS
Number of compositions of n into parts p where 5 <= p <= 14. [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 (0,0,0,0,1,1,1,1,1,1,1,1,1,1).
FORMULA
a(n) = a(n-5) +a(n-6) +a(n-7) +a(n-8) +a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) for n>13. - Vincenzo Librandi, Jun 27 2013
MATHEMATICA
CoefficientList[Series[1 / (1 - Total[x^Range[5, 14]]), {x, 0, 60}], x] (* Vincenzo Librandi, Jun 27 2013 *)
LinearRecurrence[{0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 3, 4, 5}, 50] (* Harvey P. Dale, Apr 23 2016 *)
PROG
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13-x^14))); /* or */ I:=[1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 3, 4, 5]; [n le 14 select I[n] else Self(n-5)+Self(n-6)+Self(n-7)+Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13)+Self(n-14): n in [1..70]]; // Vincenzo Librandi, Jun 27 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved