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,-2,-2,3,-1).
FORMULA
a(n) = (-1+(-1)^n+6*n^2+12*n^3)/8.
a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5) for n>4.
G.f.: x*(x+2)*(x^2+4*x+1) / ((x-1)^4*(x+1)).
EXAMPLE
For n=1 the 2 partitions of 6*1 = 6 are [1,1,1,3] and [1,1,2,2].
MATHEMATICA
LinearRecurrence[{3, -2, -2, 3, -1}, {0, 2, 15, 47, 108}, 50] (* Harvey P. Dale, Mar 22 2020 *)
PROG
(PARI) concat(0, vector(40, n, k=0; forpart(p=6*n, k++, , [4, 4]); k))
(PARI) concat(0, Vec(x*(x+2)*(x^2+4*x+1)/((x-1)^4*(x+1)) + O(x^100)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Mar 25 2015
STATUS
approved