OFFSET
0,3
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-5,0,5,-3,-3,5,0,-5,4,-1).
FORMULA
G.f.: x*(3*x^7+14*x^6+21*x^5+21*x^4+22*x^3+19*x^2+7*x+1) / ((x-1)^6*(x+1)*(x^4+x^3+x^2+x+1)).
EXAMPLE
For n=2, the 11 partitions of 12 are Xs = [7,1,1,1,1,1], [6,2,1,1,1,1], [5,3,1,1,1,1], [4,4,1,1,1,1], [5,2,2,1,1,1], [4,3,2,1,1,1], [3,3,3,1,1,1], [4,2,2,2,1,1], [3,3,2,2,1,1], [3,2,2,2,2,1] and [2,2,2,2,2,2].
MATHEMATICA
CoefficientList[Series[x (3 x^7 + 14 x^6 + 21 x^5 + 21 x^4 + 22 x^3 + 19 x^2 + 7 x + 1) / ((x - 1)^6 (x + 1) (x^4 + x^3 + x^2 + x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 20 2015 *)
PROG
(PARI)
concat(0, Vec(x*(3*x^7+14*x^6+21*x^5+21*x^4+22*x^3+19*x^2+7*x+1)/((x-1)^6*(x+1)*(x^4+x^3+x^2+x+1)) + O(x^100)))
(PARI)
concat(0, vector(35, n, k=0; forpart(p=6*n, k++, , [6, 6]); k)) \\ Colin Barker, Mar 21 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Mar 19 2015
STATUS
approved