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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.


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. 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. 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, Solomon W. Golomb, and David A. Klarner, Polyominoes. (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.

Gill Barequet, Mirah Shalah, Improved Bounds on the Growth Constant of Polyiamonds, 32nd European Workshop on Computational Geometry, 2016.

Gill Barequet, Mira Shalah, Yufei Zheng, An Improved Lower Bound on the Growth Constant of Polyiamonds, In: Cao Y., Chen J. (eds) Computing and Combinatorics, COCOON 2017, Lecture Notes in Computer Science, vol 10392.

A. J. Guttmann (ed.), Polygons, Polyominoes and Polycubes, Lecture Notes in Physics, 775 (2009). (Table 16.11, p. 479 has 75 terms of this sequence.)

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

H. Redelmeier, Emails to N. J. A. Sloane, 1991


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 March 22 04:11 EDT 2018. Contains 301047 sequences. (Running on oeis4.)