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
Arthur O'Dwyer, Polyomino strips, snakes, and ouroboroi (gives the first 32 terms)
Arthur O'Dwyer, C++ program
PROG
(C++) // see Links section
CROSSREFS
A151514 counts 1-sided snake polyominoes with k=n cells. A359707 added to A151514 gives the number of 1-sided polyominoes in which each cell has at most 2 (Von Neumann) neighbors.
A359706 counts free (2-sided) 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 14-cell ouroboroi are
### #### ### ###
# # # ## # # # ##
# ## ## # # ## # #
# # #### ## # # #
#### ### ####
and their mirror-reflections.
KEYWORD
nonn,more
AUTHOR
Arthur O'Dwyer, Jan 11 2023
STATUS
approved