A001207 - OEIS

%I M2897 N1162 #53 Aug 31 2024 09:51:34

%S 1,3,11,44,186,814,3652,16689,77359,362671,1716033,8182213,39267086,

%T 189492795,918837374,4474080844,21866153748,107217298977,527266673134,

%U 2599804551168,12849503756579,63646233127758,315876691291677,1570540515980274,7821755377244303,39014584984477092,194880246951838595,974725768600891269,4881251640514912341,24472502362094874818,122826412768568196148,617080993446201431307,3103152024451536273288,15618892303340118758816,78679501136505611375745

%N Number of fixed hexagonal polyominoes with n cells.

%D A. J. Guttmann, ed., Polygons, Polyominoes and Polycubes, Springer, 2009, p. 477. (Table 16.9 has 46 terms of this sequence.)

%D W. F. Lunnon, Counting hexagonal and triangular polyominoes, pp. 87-100 of R. C. Read, editor, Graph Theory and Computing. Academic Press, NY, 1972.

%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).

%H Vaclav Kotesovec, <a href="/A001207/b001207.txt">Table of n, a(n) for n = 1..46</a> (from reference by A. J. Guttmann)

%H Moa Apagodu, <a href="https://arxiv.org/abs/math/0202295">Counting hexagonal lattice animals</a>, arXiv:math/0202295 [math.CO], 2002-2009.

%H Gill Barequet, Solomon W. Golomb, and David A. Klarner, <a href="http://www.csun.edu/~ctoth/Handbook/chap14.pdf">Polyominoes</a>. (This is a revision, by G. Barequet, of the chapter of the same title originally written by the late D. A. Klarner for the first edition, and revised by the late S. W. Golomb for the second edition.) Preprint, 2016.

%H M. Bousquet-Mélou and A. Rechnitzer, <a href="https://doi.org/10.1016/S0012-365X(02)00352-7">Lattice animals and heaps of dimers</a>, Discrete Mathematics, Volume 258, Issues 1-3, 6 December 2002, Pages 235-274.

%H Greg Malen, Érika Roldán, and Rosemberg Toalá-Enríquez, <a href="https://doi.org/10.1007/s00026-022-00631-1">Extremal {p, q}-Animals</a>, Ann. Comb. (2023), p. 3.

%H Stephan Mertens, Markus E. Lautenbacher, <a href="https://doi.org/10.1007/BF01060088">Counting lattice animals: a parallel attack</a>, J. Statist. Phys. 66 (1992), no. 1-2, 669-678.

%H H. Redelmeier, <a href="/A006770/a006770.pdf">Emails to N. J. A. Sloane, 1991</a>

%H M. F. Sykes, M. Glen. <a href="https://doi.org/10.1088/0305-4470/9/1/014">Percolation processes in two dimensions. I. Low-density series expansions</a>, J. Phys A 9 (1) (1976) 87.

%H Markus Voege and Anthony J. Guttmann, <a href="https://doi.org/10.1016/S0304-3975(03)00229-9">On the number of hexagonal polyominoes</a>, Theoretical Computer Sciences, 307(2) (2003), 433-453. (Table 2 has 35 terms of this sequence.)

%Y Cf. A000228 (free), A006535 (one-sided).

%Y Cf. A121220 (simply connected), A059716 (column convex).

%K nonn,nice

%O 1,2

%A _N. J. A. Sloane_

%E 3 more terms and reference from _Achim Flammenkamp_, Feb 15 1999

%E More terms from Markus Voege (markus.voege(AT)inria.fr), Mar 25 2004