OFFSET
0,16
COMMENTS
Number of compositions of n into parts p where 7 <= p <= 13. [Joerg Arndt, Jun 28 2013]
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1,1,1,1,1,1,1).
FORMULA
a(n) = a(n-7) +a(n-8) +a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) for n>12. - Vincenzo Librandi, Jun 28 2013
MATHEMATICA
CoefficientList[Series[1 / (1 - Total[x^Range[7, 13]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 28 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1}, 60] (* Harvey P. Dale, Feb 25 2018 *)
PROG
(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^7-x^8-x^9-x^10-x^11-x^12-x^13))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ]; [n le 13 select I[n] else Self(n-7)+Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13): n in [1..70]]; // Vincenzo Librandi, Jun 28 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved