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A001420
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Number of fixed 2-dimensional triangular-celled animals with n cells (n-iamonds, polyiamonds) in the 2-dimensional hexagonal lattice.
(Formerly M0806 N0305)
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3
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2, 3, 6, 14, 36, 94, 250, 675, 1838, 5053, 14016, 39169, 110194, 311751, 886160, 2529260, 7244862, 20818498, 59994514, 173338962, 501994070, 1456891547, 4236446214, 12341035217, 36009329450, 105229462401, 307942754342, 902338712971, 2647263986022, 7775314024683, 22861250676074, 67284446545605
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OFFSET
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1,1
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COMMENTS
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The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.
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REFERENCES
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G. Aleksandrowicz and G. Barequet, Counting d-dimensional polycubes and nonrectangular planar polyominoes, Int. J. of Computational Geometry and Applications, 19 (2009), 215-229.
A. J. Guttmann, ed., Polygons, Polyominoes and Polycubes, Springer, 2009, p. 479. (Table 16.11 has 75 terms of this sequence.) [From Robert A. Russell, Nov 05 2010]
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. H. Redelmeier, personal communication.
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).
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LINKS
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Table of n, a(n) for n=1..32.
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
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CROSSREFS
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Cf. A000577, A001168, A006534, A030223, A030224.
Sequence in context: A002995 A093467 A080408 * A049339 A157100 A081293
Adjacent sequences: A001417 A001418 A001419 * A001421 A001422 A001423
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KEYWORD
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nonn,hard,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Brendan Owen (brendan_owen(AT)yahoo.com), Dec 15, 2001
a(28) from Joseph Myers, Sep 24 2002
a(29)-a(31) from the Aleksandrowicz and Barequet paper (N. J. A. Sloane, Jul 09 2009)
Slightly edited by Gill Barequet, May 24 2011
a(32) from Paul Church, Oct 06 2011
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STATUS
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approved
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