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A000228 Number of hexagonal polyominoes (or planar polyhexes) with n cells.
(Formerly M2682 N1072)
+0
34
1, 1, 3, 7, 22, 82, 333, 1448, 6572, 30490, 143552, 683101, 3274826, 15796897, 76581875, 372868101, 1822236628, 8934910362, 43939164263, 216651036012, 1070793308942 (list; graph; listen)
OFFSET

1,3

REFERENCES

A. T. Balaban and F. Harary, Chemical graphs V: enumeration and proposed nomenclature of benzenoid cata-condensed polycyclic aromatic hydrocarbons, Tetrahedron 24 (1968), 2505-2516.

A. T. Balaban and Paul von R. Schleyer, "Graph theoretical enumeration of polymantanes", Tetrahedron, (1978), vol. 34, 3599-3609

M. Gardner, Polyhexes and Polyaboloes. Ch. 11 in Mathematical Magic Show. New York: Vintage, pp. 146-159, 1978.

M. Gardner, Tiling with Polyominoes, Polyiamonds and Polyhexes. Chap. 14 in Time Travel and Other Mathematical Bewilderments. New York: W. H. Freeman, pp. 175-187, 1988.

F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinb. Math. Soc. (2) 17 (1970), 1-13.

D. A. Klarner, Cell growth problems, Canad. J. Math., 19 (1967), 851-863.

J. V. Knop et al., On the total number of polyhexes, Match, No. 16 (1984), 119-134.

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

N. Trinajstich, Z. Jerievi, J. V. Knop, W. R. Muller and K. Szymanski, COMPUTER GENERATION OF ISOMERIC STRUCTURES, Pure & Appl. Chem., Vol. 55, No. 2, pp. 379-39O, 1983.

Jaime Rangel-Mondragon, Polyominoes and Related Families, The Mathematica Journal, 9:3 (2005), 609-640.

LINKS

Ed Pegg, Jr., Illustrations of polyforms

A. Clarke, Polycubes

D. Gouyou-Beauchamps and P. Leroux, Enumeration of symmetry classes of convex polyominoes on the honeycomb lattice.

M. Keller, Counting polyforms

Joseph Myers, Polyomino, polyhex and polyiamond tiling

N. J. A. Sloane, Illustration of initial terms

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

CROSSREFS

Equals (A006535 + A030225)/2.

Cf. A036359, A002216, A005963, A000228, A001998, A018190.

Cf. A001207, A057973.

Adjacent sequences: A000225 A000226 A000227 this_sequence A000229 A000230 A000231

Sequence in context: A070766 A111772 A018190 this_sequence A108070 A038147 A082271

KEYWORD

nonn,nice,hard

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

a(13) from Achim Flammenkamp (achim(AT)uni-bielefeld.de) Feb 15 1999. a(14) from Brendan Owen, Dec 31, 2001

a(15) from Joseph Myers (jsm(AT)polyomino.org.uk), May 05 2002

a(16)-a(20) from Joseph Myers (jsm(AT)polyomino.org.uk), Sep 21 2002

a(21) from Herman Jamke (hermanjamke(AT)fastmail.fm), May 05 2007

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Last modified July 4 09:27 EDT 2009. Contains 160562 sequences.


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