%I #37 Sep 13 2023 23:17:25

%S 1,2,6,86,7626,3956996,8326366368,69277957195904,2287898999182608384,

%T 301053169143557925650432,158147142250171927345054089216,

%U 331982638848895606930198405868158976,2786232352655643085145552249123037486514176

%N Number of distinct binary arrays of size n X n with respect to isometric transformations.

%H Johnny Sammon, <a href="/A364794/a364794_3.pdf">Counting Distinct Binary Arrays With Respect To Isometric Transformations</a>.

%e For n = 2, the a(2) = 6 distinct binary arrays are

%e OO XO XX XO XX XX

%e OO OO OO OX XO XX

%e For n = 4

%e OOXX OOXO

%e OXXO is considered equivalent to XXXX

%e OOXO OOOX

%e OOXO OOOO

%e because we can rotate the bounding box of the Xs 90 degrees clockwise and place it back into the array as given above.

%Y Cf. A054247 (without shift), A255016 (on n X n torus).

%K nonn,more

%O 0,2

%A _Johnny Sammon_, Aug 08 2023