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 A359707 Number of 1-sided ouroboros polyominoes with k=2n cells. 2
 0, 1, 0, 1, 1, 4, 11, 45, 178, 762, 3309, 14725, 66323, 302342, 1391008, 6453950 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=1..16. 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. Sequence in context: A149289 A149290 A074410 * A363663 A149291 A149292 Adjacent sequences: A359704 A359705 A359706 * A359708 A359709 A359710 KEYWORD nonn,more AUTHOR Arthur O'Dwyer, Jan 11 2023 STATUS approved

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Last modified September 28 23:23 EDT 2023. Contains 365739 sequences. (Running on oeis4.)