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

0,2

Links

Table of n, a(n) for n=0..10.

Formula

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

Example

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.

Sequence in context: A317899 A076936 A344536 * A303085 A086482 A078758

Adjacent sequences: A348564 A348565 A348566 * A348568 A348569 A348570

Keyword

nonn,more

Author

Andrey Zabolotskiy, Oct 22 2021

Status

approved