A364794 Number of distinct binary arrays of size n X n with respect to isometric transformations.

1, 2, 6, 86, 7626, 3956996, 8326366368, 69277957195904, 2287898999182608384, 301053169143557925650432, 158147142250171927345054089216, 331982638848895606930198405868158976, 2786232352655643085145552249123037486514176

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Johnny Sammon, Counting Distinct Binary Arrays With Respect To Isometric Transformations.

Example

For n = 2, the a(2) = 6 distinct binary arrays are
  OO  XO  XX  XO  XX  XX
  OO  OO  OO  OX  XO  XX
For n = 4
  OOXX                                OOXO
  OXXO  is considered equivalent to   XXXX
  OOXO                                OOOX
  OOXO                                OOOO
because we can rotate the bounding box of the Xs 90 degrees clockwise and place it back into the array as given above.

Crossrefs

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

Sequence in context: A109892 A268534 A055702 * A334779 A305598 A179214

Adjacent sequences: A364791 A364792 A364793 * A364795 A364796 A364797

Keyword

nonn,more

Author

Johnny Sammon, Aug 08 2023

Status

approved