OFFSET
0,7
COMMENTS
Number of compositions (ordered partitions) of n into parts 3, 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 (0,0,1,1,1,1,1,1).
FORMULA
a(n) = a(n-3) +a(n-4) +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[3, 8]]), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 27 2013 *)
LinearRecurrence[{0, 0, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 1, 1, 1, 2, 3}, 60] (* Harvey P. Dale, Mar 29 2022 *)
PROG
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x^3-x^4-x^5-x^6-x^7-x^8)))); /* or */ I:=[1, 0, 0, 1, 1, 1, 2, 3]; [n le 8 select I[n] else Self(n-3)+Self(n-4)+Self(n-5)+Self(n-6)+Self(n-7)+Self(n-8): n in [1..50]]; // Vincenzo Librandi, Jun 27 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved