A343096 Number of n-colorings of an n X n grid, up to rotational symmetry.

1, 1, 6, 4995, 1073758336, 74505806274453125, 2578606199622659276537193216, 64230894380264719522488136461023341060807, 1569275433846670190958947355821723644654155086251882971136, 49156762618888228404518977131728029071108432602235970059344750602021716398409

Offset: 0

Author

Andrew Howroyd, Apr 14 2021

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..25
• Peter Kagey and William Keehn, Counting Tilings of the n X m Grid, Cylinder, and Torus, J. Int. Seq. (2024) Vol. 27, Art. No. 24.6.1. See p. 2.

Crossrefs

Main diagonal of A343095.

Cf. A002489.

Programs

Maple

a:= n-> (n^(n^2)+2*n^((n^2+3*(n mod 2))/4)+n^((n^2+(n mod 2))/2))/4:
seq(a(n), n=0..10);  # Alois P. Heinz, May 12 2021

PARI

a(n) = {(n^(n^2) + 2*n^((n^2 + 3*(n%2))/4) + n^((n^2 + (n%2))/2))/4}

Formula

a(n) = (n^(n^2) + 2*n^((n^2 + 3*(n mod 2))/4) + n^((n^2 + (n mod 2))/2))/4.