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A000577 Number of triangular polyominoes (or polyiamonds) with n cells (turning over is allowed, holes are allowed, must be connected along edges).
(Formerly M2374 N0941)
+0
29
1, 1, 1, 3, 4, 12, 24, 66, 160, 448, 1186, 3334, 9235, 26166, 73983, 211297, 604107, 1736328, 5000593, 14448984, 41835738, 121419260, 353045291, 1028452717, 3000800627, 8769216722, 25661961898, 75195166667 (list; graph; listen)
OFFSET

1,4

REFERENCES

F. Harary, Graphical enumeration problems; in Graph Theory and Theoretical Physics, ed. F. Harary, Academic Press, London, 1967, pp. 1-41.

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

P. J. Torbijn, Polyiamonds, J. Rec. Math., 2 (1969), 216-227.

Ed Pegg, Jr., Polyform puzzles, in Tribute to a Mathemagician, Peters, 2005, pp. 119-125.

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

LINKS

A. Clarke, Polyiamonds

S. T. Coffin, The Puzzling World of Polyhedral Dissections, Chap 2, Table 1.

R. K. Guy, O'Beirne's Hexiamond, in The Mathemagician and the Pied Puzzler - A Collection in Tribute to Martin Gardner, Ed. E. R. Berlekamp and T. Rogers, A. K. Peters, 1999, 85-96.

J. and J. Hindriks, Dutchman Designs: Quilting Patterns

Kadon Enterprises, The 66 polyominoes of order 8 (from a puzzle)

Kadon Enterprises, Home page

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

M. Keller, Counting polyforms

CROSSREFS

Cf. A006534, A030223, A030224, A001420, A096361.

Adjacent sequences: A000574 A000575 A000576 this_sequence A000578 A000579 A000580

Sequence in context: A073713 A084921 A070765 this_sequence A111758 A000942 A000207

KEYWORD

nonn,hard,nice

AUTHOR

njas

EXTENSIONS

More terms from David W. Wilson (davidwwilson(AT)comcast.net). a(19) from Achim Flammenkamp (achim(AT)uni-bielefeld.de) Feb 15 1999.

a(20), a(21), a(22), a(23) and a(24) from Brendan Owen (brendan_owen(AT)yahoo.com), Jan 01 2002

a(25) to a(28) from Joseph Myers (jsm(AT)polyomino.org.uk), Sep 24 2002

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Last modified October 11 13:47 EDT 2008. Contains 144830 sequences.


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