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%I #12 Dec 21 2022 04:34:54
%S 1,4,2,32,12,832,232,69632,14416,18719744,2876576
%N Number of fully symmetric recurrent sandpiles on an n X n grid.
%F A256046(n) divides a(n), a(n) divides A348566(n, n).
%e a(0) = 1, the empty sandpile on an empty grid.
%e a(1) = 4, all 4 sandpiles on a 1 X 1 grid are fully symmetric.
%e a(2) = 2 fully symmetric recurrent sandpiles on an 2 X 2 grid are the all-2 and all-3 sandpiles.
%e Among A348566(4, 4) = 36 sandpiles with horizontal and vertical symmetry, only a(4) = 12 also have diagonal symmetries:
%e 3333 1331 1331 3223 3223 3333 2222 0330 2332 2332 0330 2222
%e 3333 3223 3333 2222 2332 3223 2222 3223 3223 3333 3333 2332
%e 3333 3223 3333 2222 2332 3223 2222 3223 3223 3333 3333 2332
%e 3333 1331 1331 3223 3223 3333 2222 0330 2332 2332 0330 2222
%Y Cf. A348566, A256046.
%K nonn,more
%O 0,2
%A _Andrey Zabolotskiy_, Oct 22 2021
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