A200564 a(n) = (2^(n^2)+2^((n^2+n)/2))/2.

1, 2, 12, 288, 33280, 16793600, 34360786944, 281475110928384, 9223372071214514176, 1208925819632221360750592, 633825300114132715146861084672, 1329227995784915909797295207699447808, 11150372599265311570918974863776009399828480

Offset

0,2

Comments

The number of inequivalent n x n black and white checkerboards where two boards are indistinguishable if and only if they are identical after being reflected about the main diagonal.

Cycle index = (s_1^(n^2) + s_1^n*s_2^((n^2-n)/2))/2.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..57

Peter Kagey and William Keehn, Counting tilings of the n X m grid, cylinder, and torus, arXiv:2311.13072 [math.CO], 2023. See p. 3.

Mathematica

Table[(2^(n^2)+2^((n^2+n)/2))/2, {n, 0, 10}]

Prog

(PARI) a(n)=2^(n^2-1) + 2^((n^2+n)/2-1) \\ Charles R Greathouse IV, Dec 08 2022

Crossrefs

Sequence in context: A211937 A176037 A057170 * A008338 A000178 A108395

Adjacent sequences: A200561 A200562 A200563 * A200565 A200566 A200567

Keyword

nonn,easy

Author

Geoffrey Critzer, Nov 19 2011

Status

approved