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Filaments with n square cells.
(Formerly M0835 N0317)
9

%I M0835 N0317 #39 Dec 15 2022 17:01:01

%S 1,1,1,2,3,7,13,31,65,154,347,824,1905,4512,10546,24935,58476,138002,

%T 323894,763172,1790585,4213061,9878541,23214728,54393063,127687369,

%U 298969219,701171557,1640683309,3844724417,8991137036,21054243655,49211076053

%N Filaments with n square cells.

%C Or, number of 2-sided snake polyominoes with n cells. - _Ed Pegg Jr_, May 13 2009

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%D R. C. Tilley, R. G. Stanton and D. D. Cowan, The cell growth problem for filaments, pp. 310-339 in Proceedings of the Louisiana Conference on Combinatorics, Graph Theory and Computer Science. Vol. 1, edited R. C. Mullin et al., 1970.

%H Arthur O'Dwyer, <a href="https://quuxplusone.github.io/blog/2022/12/08/polyomino-snakes/">Polyomino strips, snakes, and ouroboroi</a>, Dec 10 2022.

%H Ed Pegg, Jr., <a href="http://demonstrations.wolfram.com/PolyformExplorer/">Illustrations of polyforms</a>

%H Herman Tulleken, <a href="https://www.researchgate.net/publication/333296614_Polyominoes">Polyominoes 2.2: How they fit together</a>, (2019).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Polyomino.html">Polyomino</a>

%Y A333313 counts 2-sided (free) "strip" polyominoes; that is, snakes with no holes.

%K nonn

%O 0,4

%A _N. J. A. Sloane_

%E a(23) from _Joseph Myers_, Nov 22 2010

%E a(24)-a(26) from _Sean A. Irvine_, May 21 2013

%E a(27)-a(32) from _John Mason_, Dec 05 2021