OFFSET
0,3
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-2,0,0,1,1,-1).
FORMULA
G.f.: x*(5*x^7+13*x^6+24*x^5+29*x^4+28*x^3+17*x^2+8*x+1) / ((x-1)^4*(x+1)^2*(x^2+1)*(x^2+x+1)).
EXAMPLE
For n=2 the 9 partitions of 5*2 = 10 are [1,1,1,7], [1,1,2,6], [1,1,3,5], [1,1,4,4], [1,2,2,5], [1,2,3,4], [1,3,3,3], [2,2,2,4] and [2,2,3,3].
PROG
(PARI) concat(0, vector(40, n, k=0; forpart(p=5*n, k++, , [4, 4]); k))
(PARI) concat(0, Vec(x*(5*x^7+13*x^6+24*x^5+29*x^4+28*x^3+17*x^2+8*x+1) / ((x-1)^4*(x+1)^2*(x^2+1)*(x^2+x+1)) + O(x^100)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Mar 25 2015
STATUS
approved