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A343096
Number of n-colorings of an n X n grid, up to rotational symmetry.
2
1, 1, 6, 4995, 1073758336, 74505806274453125, 2578606199622659276537193216, 64230894380264719522488136461023341060807, 1569275433846670190958947355821723644654155086251882971136, 49156762618888228404518977131728029071108432602235970059344750602021716398409
OFFSET
0,3
LINKS
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.
FORMULA
a(n) = (n^(n^2) + 2*n^((n^2 + 3*(n mod 2))/4) + n^((n^2 + (n mod 2))/2))/4.
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
PROG
(PARI) a(n) = {(n^(n^2) + 2*n^((n^2 + 3*(n%2))/4) + n^((n^2 + (n%2))/2))/4}
CROSSREFS
Main diagonal of A343095.
Cf. A002489.
Sequence in context: A268504 A099723 A226499 * A066061 A028366 A305886
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Apr 14 2021
STATUS
approved