A348567 Number of fully symmetric recurrent sandpiles on an n X n grid.

1, 4, 2, 32, 12, 832, 232, 69632, 14416, 18719744, 2876576

Offset: 0

Author

Andrey Zabolotskiy, Oct 22 2021

Keywords

• nonn
• more

Examples

			a(0) = 1, the empty sandpile on an empty grid.
a(1) = 4, all 4 sandpiles on a 1 X 1 grid are fully symmetric.
a(2) = 2 fully symmetric recurrent sandpiles on an 2 X 2 grid are the all-2 and all-3 sandpiles.
Among A348566(4, 4) = 36 sandpiles with horizontal and vertical symmetry, only a(4) = 12 also have diagonal symmetries:
  3333  1331  1331  3223  3223  3333  2222  0330  2332  2332  0330  2222
  3333  3223  3333  2222  2332  3223  2222  3223  3223  3333  3333  2332
  3333  3223  3333  2222  2332  3223  2222  3223  3223  3333  3333  2332
  3333  1331  1331  3223  3223  3333  2222  0330  2332  2332  0330  2222
		

Crossrefs

Cf. A348566, A256046.

Formula

A256046(n) divides a(n), a(n) divides A348566(n, n).