A047938 Number of ways to label points of an n X n grid with 3 colors, up to rotational symmetry.

1, 3, 24, 4995, 10763361, 211822552035, 37523658921114744, 59824832307866205347043, 858420955073128584419531008641, 110856622060759442496180656754310346403, 128844380183002832759115461915902241562318377784, 1347757724935823407809884872163997148505019182125807296675

Offset: 0

Author

Rob Pratt

Keywords

• nonn

Comments

Labels of adjacent points need not be distinct.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..25

Crossrefs

Column k=3 of A343095.

See A068253 for number of proper colorings.

Cf. A054739, A047937, A047939.

Formula

a(n) = (m^(n^2) + 2 m^((n^2 + 3 (n mod 2))/4) + m^((n^2 + (n mod 2))/2))/4, with m = 3.

Extensions

Terms a(10) and beyond from Andrew Howroyd, Apr 14 2021