OFFSET
0,5
COMMENTS
Number of compositions of n into parts p where 2 <= p < = 9. [Joerg Arndt, Jun 24 2013]
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
R. Mullen, On Determining Paint by Numbers Puzzles with Nonunique Solutions, JIS 12 (2009) 09.6.5
Index entries for linear recurrences with constant coefficients, signature (0, 1, 1, 1, 1, 1, 1, 1, 1).
FORMULA
a(0)=1, a(1)=0, a(2)=1, a(3)=1, a(4)=2, a(5)=3, a(6)=5, a(7)=8, a(8)=13, a(n)=a(n-2)+a(n-3)+a(n-4)+a(n-5)+a(n-6)+a(n-7)+a(n-8)+a(n-9). - Harvey P. Dale, Dec 17 2013
MATHEMATICA
CoefficientList[Series[1 / (1 - x^2 - x^3 - x^4 - x^5 - x^6 - x^7 - x^8 - x^9), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 24 2013 *)
CoefficientList[Series[1/(1-Total[x^Range[2, 9]]), {x, 0, 40}], x] (* or *) LinearRecurrence[{0, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 1, 1, 2, 3, 5, 8, 13}, 40] (* Harvey P. Dale, Dec 17 2013 *)
PROG
(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9))); // Vincenzo Librandi, Jun 24 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved