This site is supported by donations to The OEIS Foundation.



Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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.


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, http://www.csun.edu/~ctoth/Handbook/chap14.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.

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

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



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 23 00:33 EST 2017. Contains 295107 sequences.