A002013 Number of filaments with n square cells. (Formerly M0835 N0317)

1, 1, 1, 2, 3, 7, 13, 31, 65, 154, 347, 824, 1905, 4512, 10546, 24935, 58476, 138002, 323894, 763172, 1790585, 4213061, 9878541, 23214728, 54393063, 127687369, 298969219, 701171557, 1640683309, 3844724417, 8991137036, 21054243655, 49211076053, 115161584232, 269046285809, 629247427101

Offset

0,4

Comments

Or, number of 2-sided snake polyominoes with n cells. - Ed Pegg Jr, May 13 2009

References

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

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

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.

Links

Table of n, a(n) for n=0..35.

Arthur O'Dwyer, Polyomino strips, snakes, and ouroboroi, Dec 10 2022.

Ed Pegg, Jr., Illustrations of polyforms

Herman Tulleken, Polyominoes 2.2: How they fit together, (2019).

Eric Weisstein's World of Mathematics, Polyomino

Crossrefs

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

A182644 counts fixed snake polyominoes.

A003104 is the polyhex analog.

Sequence in context: A102644 A014234 A124430 * A171416 A193530 A003120

Adjacent sequences: A002010 A002011 A002012 * A002014 A002015 A002016

Keyword

nonn

Author

N. J. A. Sloane

Extensions

a(23) from Joseph Myers, Nov 22 2010

a(24)-a(26) from Sean A. Irvine, May 21 2013

a(27)-a(32) from John Mason, Dec 05 2021

a(33)-a(35) from Dat Truong and Christian Barrientos, Dec 16 2025

Status

approved