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,-3,2,-3,4,-4,3,-2,3,-3,1).
FORMULA
G.f.: -x^2*(2*x^6+4*x^5+6*x^4+6*x^3+7*x^2+4*x+3) / ((x-1)^5*(x^2+x+1)*(x^4+x^3+x^2+x+1)).
a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 4*a(n-5) - 4*a(n-6) + 3*a(n-7) - 2*a(n-8) + 3*a(n-9) - 3*a(n-10) + a(n-11). - Wesley Ivan Hurt, Jun 26 2025
EXAMPLE
For n=2 the 3 partitions of 4*2 = 8 are [1,1,1,1,4], [1,1,1,2,3] and [1,1,2,2,2].
PROG
(PARI) concat(0, vector(40, n, k=0; forpart(p=4*n, k++, , [5, 5]); k))
(PARI) concat([0, 0], Vec(-x^2*(2*x^6+4*x^5+6*x^4+6*x^3+7*x^2+4*x+3)/((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, Mar 23 2015
STATUS
approved