A362291 Number of pairs of disjoint subsets of 1..n^2 of size 2*floor(n/2) having equal sum.

1, 2, 68, 26098, 1408886, 12369296230, 673890139470, 33193434883028584

Offset: 1

Author

Michael S. Branicky, Apr 14 2023

Keywords

• nonn
• hard
• more

Crossrefs

Cf. A052928, A362280.

Programs

Python

from math import factorial
from itertools import combinations as C
def a(n):
    E = [i for i in range(1, n**2+1)]
    m = n if n%2 == 0 else n-1
    return sum(1 for u in C(E, 2*m) for t in C(u, m) if 2*sum(t)==sum(u))
print([a(n) for n in range(1, 5)])

Formula

a(n) = A362280(n)/((m!)^2 * (n^2-2m)!), where m = 2*floor(n/2).

Extensions

a(6)-a(7) from Martin Ehrenstein, Apr 16 2023

a(8) from Martin Ehrenstein, Apr 25 2023