

A359707


Number of 1sided ouroboros polyominoes with k=2n cells.


2



0, 1, 0, 1, 1, 4, 11, 45, 178, 762, 3309, 14725, 66323, 302342, 1391008, 6453950
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OFFSET

1,6


COMMENTS

A "snake" polyomino is a polyomino in which exactly two cells have exactly one (Von Neumann) neighbor apiece, and the rest have two neighbors apiece. Arthur O'Dwyer coined the term "ouroboros polyomino" for a polyomino in which every cell has exactly two neighbors: that is, an ouroboros polyomino is like a "snake" in which the head cell neighbors the tail cell.
A324407 etc. use the term "polyomino ring" in place of "ouroboros polyomino."
A checkerboard coloring shows that every ouroboros must have an even number of cells.


LINKS



PROG

(C++) // see Links section


CROSSREFS

A151514 counts 1sided snake polyominoes with k=n cells. A359707 added to A151514 gives the number of 1sided polyominoes in which each cell has at most 2 (Von Neumann) neighbors.
A359706 counts free (2sided) ouroboros polyominoes with k=2n cells. A359707 minus A359706 gives the count of chiral pairs. This sequence first differs from A359706 at k=14; the four chiral pairs of 14cell ouroboroi are
### #### ### ###
# # # ## # # # ##
# ## ## # # ## # #
# # #### ## # # #
#### ### ####
and their mirrorreflections.


KEYWORD

nonn,more


AUTHOR



STATUS

approved



