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A001420 Number of fixed 2-dimensional triangular-celled animals with n cells (n-iamonds, polyiamonds) in the 2-dimensional hexagonal lattice.
(Formerly M0806 N0305)
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 (list; graph; refs; listen; history; text; internal format)



The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.


G. Aleksandrowicz and G. Barequet, Counting d-dimensional polycubes and nonrectangular planar polyominoes, Int. J. of Computational Geometry and Applications, 19 (2009), 215-229.

Gill Barequet, M Shalah, Improved Bounds on the Growth Constant of Polyiamonds, 32nd European Workshop on Computational Geometry, 2016; http://www.eurocg2016.usi.ch/sites/default/files/paper_19.pdf

A. J. Guttmann, ed., Polygons, Polyominoes and Polycubes, Springer, 2009, p. 479. (Table 16.11 has 75 terms of this sequence.)

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).


Table of n, a(n) for n=1..32.

G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2


Cf. A000577, A001168, A006534, A030223, A030224.

Sequence in context: A246640 A080408 A275774 * A049339 A157100 A081293

Adjacent sequences:  A001417 A001418 A001419 * A001421 A001422 A001423




N. J. A. Sloane.


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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Last modified May 27 19:12 EDT 2017. Contains 287207 sequences.