OFFSET
0,2
COMMENTS
a(n) is the number of partitions of n*(12*n+1) into 2*n distinct parts <=12*n.
EXAMPLE
a(1) = 6 because there are 6 2-element subsets that can be chosen from {1,2,...,12} having element sum 13: {1,12}, {2,11}, {3,10}, {4,9}, {5,8}, {6,7}.
MAPLE
b:= proc(n, i, t) option remember;
`if`(i<t or n<t*(t+1)/2 or n>t*(2*i-t+1)/2, 0,
`if`(n=0, 1, b(n, i-1, t) +`if`(n<i, 0, b(n-i, i-1, t-1))))
end:
a:= n-> b(n*(12*n+1), 12*n, 2*n):
seq(a(n), n=0..12);
MATHEMATICA
b[n_, i_, t_] /; i<t || n<t(t+1)/2 || n>t(2i-t+1)/2 = 0; b[0, _, _] = 1;
b[n_, i_, t_] := b[n, i, t] = b[n, i-1, t] + If[n<i, 0, b[n-i, i-1, t-1]];
a[n_] := b[n(12n+1), 12n, 2n];
a /@ Range[0, 10] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 18 2012
STATUS
approved