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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)
35
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; text; internal format)
OFFSET

1,4

COMMENTS

If holes are not allowed, we get A070765. - Joseph Myers, Apr 20 2009

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.

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.

LINKS

Table of n, a(n) for n=1..30.

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 [broken link?]

J. and J. Hindriks, Dutchman Designs: Quilting Patterns [broken link?]

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

Kadon Enterprises, Home page

M. Keller, Counting polyforms

R. J. Mathar, Illustrations for up to 9-iamonds

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

Eric Weisstein's World of Mathematics, Polyiamond

CROSSREFS

Cf. A000207, A006534, A030223, A030224, A001420, A096361, A070765.

Cf. also A000105, A000228, A103465.

Sequence in context: A291023 A084921 A070765 * A111758 A264484 A000942

Adjacent sequences:  A000574 A000575 A000576 * A000578 A000579 A000580

KEYWORD

nonn,hard,more,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from David W. Wilson

a(19) from Achim Flammenkamp, 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, Sep 24 2002

Link updated by William Rex Marshall, Dec 16 2009

a(29) and a(30) from Joseph Myers, Nov 21 2010

STATUS

approved

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Last modified May 22 17:42 EDT 2018. Contains 304426 sequences. (Running on oeis4.)