cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A359707 Number of 1-sided ouroboros polyominoes with k=2n cells.

This page as a plain text file.
%I A359707 #12 Jan 18 2023 09:36:27
%S A359707 0,1,0,1,1,4,11,45,178,762,3309,14725,66323,302342,1391008,6453950
%N A359707 Number of 1-sided ouroboros polyominoes with k=2n cells.
%C A359707 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.
%C A359707 A324407 etc. use the term "polyomino ring" in place of "ouroboros polyomino."
%C A359707 A checkerboard coloring shows that every ouroboros must have an even number of cells.
%H A359707 Arthur O'Dwyer, <a href="https://quuxplusone.github.io/blog/2022/12/08/polyomino-snakes/">Polyomino strips, snakes, and ouroboroi</a> (gives the first 32 terms)
%H A359707 Arthur O'Dwyer, <a href="https://quuxplusone.github.io/blog/code/2022-12-08-polyomino-snakes-and-strips.cpp">C++ program</a>
%o A359707 (C++) // see Links section
%Y A359707 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.
%Y A359707 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
%Y A359707     ###   ####   ###   ###
%Y A359707     # #   #  ##  # #   # ##
%Y A359707     # ##  ##  #  # ##  #  #
%Y A359707     #  #   ####  ## #  #  #
%Y A359707     ####          ###  ####
%Y A359707 and their mirror-reflections.
%K A359707 nonn,more
%O A359707 1,6
%A A359707 _Arthur O'Dwyer_, Jan 11 2023