OFFSET
0,3
COMMENTS
a(n) is the number of partitions of n^3 into n distinct parts <= 2*n^2.
EXAMPLE
a(0) = 1: {}.
a(1) = 1: {1}.
a(2) = 3: {1,7}, {2,6}, {3,5}.
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^3, 2*n^2, n):
seq(a(n), n=0..12);
MATHEMATICA
$RecursionLimit = 2000;
b[n_, i_, t_] := b[n, i, t] = If[i<t || n<t (t+1)/2 || n>t (2i-t+1)/2, 0, If[n==0, 1, b[n, i-1, t] + If[n<i, 0, b[n-i, i-1, t-1]]]];
a[n_] := b[n^3, 2n^2, n];
a /@ Range[0, 17] (* Jean-François Alcover, Dec 05 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 21 2012
STATUS
approved