OFFSET
0,3
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,3,-6,7,-6,6,-6,7,-6,3,-3,3,-1).
FORMULA
G.f.: x^2*(x+1)^2*(x^2+1)*(x^4+2*x^3+2*x^2+x+2) / ((x-1)^6*(x^2+x+1)^2*(x^4+x^3+x^2+x+1)).
EXAMPLE
For n=2 the 2 partitions of 4*2 = 8 are [1,1,1,1,1,3] and [1,1,1,1,2,2].
MATHEMATICA
Table[Length[IntegerPartitions[4n, {6}]], {n, 0, 40}] (* or *) LinearRecurrence[ {3, -3, 3, -6, 7, -6, 6, -6, 7, -6, 3, -3, 3, -1}, {0, 0, 2, 11, 35, 90, 199, 391, 709, 1206, 1945, 3009, 4494, 6510}, 40] (* Harvey P. Dale, Apr 12 2018 *)
PROG
(PARI) concat(0, vector(40, n, k=0; forpart(p=4*n, k++, , [6, 6]); k))
(PARI) concat([0, 0], Vec(x^2*(x+1)^2*(x^2+1)*(x^4+2*x^3+2*x^2+x+2) / ((x-1)^6*(x^2+x+1)^2*(x^4+x^3+x^2+x+1)) + O(x^100)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Mar 23 2015
STATUS
approved