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Number of 1-sided strip polyominoes with n cells.
4

%I #40 Jan 18 2023 03:25:16

%S 1,1,2,5,10,24,52,124,282,668,1548,3654,8533,20093,47033,110533,

%T 258807,607227,1421055,3329585,7785995,18221563,42575336,99539106,

%U 232398659,542864111,1266567155,2956342341,6893180336,16078817198,37469245219,87347384305,203447081205

%N Number of 1-sided strip polyominoes with n cells.

%C A "strip" polyomino is a snake polyomino (A151514) with no holes.

%C This sequence first differs from A151514 at n = 7. An example of a polyomino counted by A151514, but not by this sequence, is:

%C ###

%C # #

%C ##

%H Arthur O'Dwyer, <a href="https://quuxplusone.github.io/blog/2022/12/08/polyomino-snakes/">Polyomino strips, snakes, and ouroboroi</a> (gives first 33 terms).

%H Arthur O'Dwyer, <a href="https://quuxplusone.github.io/blog/code/2022-12-08-polyomino-snakes-and-strips.cpp">C++ program</a>.

%o (C++) // see Links section

%Y A333313 gives the number of free (2-sided) strip polyominoes with n cells. Subtracting A333313 from A359068 gives the number of chiral pairs.

%Y A151514 gives the number of 1-sided snake polyominoes with n cells; A151514(n) > A359068(n) for n >= 7.

%Y Subtracting A359068 from A151514 gives the number of snake polyominoes with n cells that have at least one hole.

%K nonn,more

%O 1,3

%A _Arthur O'Dwyer_, Jan 11 2023