OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,2,-3,4,-4,3,-2,3,-3,1).
FORMULA
G.f.: -(x^7+4*x^6+5*x^5+7*x^4+6*x^3+6*x^2+2*x+1) / ((x-1)^5*(x^2+x+1)*(x^4+x^3+x^2+x+1)).
a(n) = A001401(4n). - Alois P. Heinz, Apr 01 2015
EXAMPLE
For n=2 the 18 partitions of 2*4 = 8 are [8], [1,7], [2,6], [3,5], [4,4], [1,1,6], [1,2,5], [1,3,4], [2,2,4], [2,3,3], [1,1,1,5], [1,1,2,4], [1,1,3,3], [1,2,2,3], [2,2,2,2], [1,1,1,1,4], [1,1,1,2,3] and [1,1,2,2,2].
PROG
(PARI) concat(1, vector(40, n, k=0; forpart(p=4*n, k++, , [1, 5]); k))
(PARI) Vec(-(x^7+4*x^6+5*x^5+7*x^4+6*x^3+6*x^2+2*x+1) / ((x-1)^5*(x^2+x+1)*(x^4+x^3+x^2+x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Apr 01 2015
STATUS
approved