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A000577
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Number of triangular polyominoes (or polyiamonds) with n cells (turning over is allowed, holes are allowed, must be connected along edges).
(Formerly M2374 N0941)
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30
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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, 220605519559, 647943626796
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| If holes are not allowed, we get A070765. - Joseph S. Myers, Apr 20 2009
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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.
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.
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).
P. J. Torbijn, Polyiamonds, J. Rec. Math., 2 (1969), 216-227.
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LINKS
| Ed Pegg, Jr., Illustrations of polyforms
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
M. Keller, Counting polyforms
Eric Weisstein's World of Mathematics, Polyiamond
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CROSSREFS
| Cf. A000207, A006534, A030223, A030224, A001420, A096361, A070765.
Sequence in context: A073713 A084921 A070765 * A111758 A000942 A197459
Adjacent sequences: A000574 A000575 A000576 * A000578 A000579 A000580
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KEYWORD
| nonn,hard,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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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
Link updated by William Rex Marshall (w.r.marshall(AT)actrix.co.nz), Dec 16 2009
a(29) and a(30) from Joseph Myers (jsm(AT)polyomino.org.uk), Nov 21 2010
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