

A000577


Number of triangular polyominoes (or triangular polyforms, or polyiamonds) with n cells (turning over is allowed, holes are allowed, must be connected along edges).
(Formerly M2374 N0941)


68



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, 1905104762320, 5607039506627, 16517895669575
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OFFSET

1,4


COMMENTS

It is a consequence of Madras's 1999 pattern theorem that almost all polyiamonds have holes, i.e., lim_{n>oo} A070765(n)/A000577(n) = 0.  Johann Peters, Jan 06 2024


REFERENCES

F. Harary, Graphical enumeration problems; in Graph Theory and Theoretical Physics, ed. F. Harary, Academic Press, London, 1967, pp. 141.
W. F. Lunnon, Counting hexagonal and triangular polyominoes, pp. 87100 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. 119125.
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), 216227.


LINKS

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, 8596 [broken link?]


CROSSREFS



KEYWORD

nonn,hard,nice


AUTHOR



EXTENSIONS

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


STATUS

approved



