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A006534
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Number of one-sided triangular polyominoes (n-iamonds) with n cells; turning over not allowed, holes are allowed.
(Formerly M3287)
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5
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1, 1, 1, 4, 6, 19, 43, 120, 307, 866, 2336, 6588, 18373, 52119, 147700, 422016, 1207477, 3471067, 9999135, 28893560, 83665729, 242826187, 706074369, 2056870697, 6001555275, 17538335077, 51323792789, 150390053432
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OFFSET
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1,4
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COMMENTS
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The figures are formed by connecting n regular triangles by edges.
"Turning over not allowed" means that axial symmetric polyiamonds are counted separately, thus a(4) = 4 and a(5) = 6 while A000577(4) = 3 and A000577(5) = 4, cf. examples. - M. F. Hasler, Nov 12 2017
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REFERENCES
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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.
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
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Table of n, a(n) for n=1..28.
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. Meeus & N. J. A. Sloane, Correspondence, 1974-1975
Ed Pegg, Jr., Illustrations of polyforms
Eric Weisstein's World of Mathematics, Polyiamond.
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EXAMPLE
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From M. F. Hasler, Nov 12 2017: (Start)
Putting dots for the approximate center of the regular triangles (alternatively flipped up and down for neighboring dots), we have:
a(4) = #{ .... , .:. , ..: , :.. } = 4, while ..: and :.. are considered equivalent and not counted twice in A000577(4) = 3.
a(5) = #{ ..... , ...: , :... , ..:. , .:.. , :.: } = 6, and again the 2nd & 3rd and 4th & 5th are considered equivalent and not counted twice in A000577(5) = 4. (End)
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CROSSREFS
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Cf. A000577 (same with "turning over allowed"), A030223, A030224, A001420.
Sequence in context: A026521 A222379 A202618 * A064035 A010364 A110391
Adjacent sequences: A006531 A006532 A006533 * A006535 A006536 A006537
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KEYWORD
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nonn,hard,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Corrected and extended by David W. Wilson.
a(19) from Achim Flammenkamp, Feb 15 1999
a(20) to a(28) from Joseph Myers, Sep 24 2002
Edited by M. F. Hasler, Nov 12 2017
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STATUS
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approved
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