A006534 Number of one-sided triangular polyominoes (n-iamonds) with n cells; turning over not allowed, holes are allowed.
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, 441210664337, 1295886453860, 3810208448847, 11214076720061, 33035788241735
Offset: 1
Examples
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)
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.
- 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
- John Mason, Table of n, a(n) for n = 1..52
- 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.
Extensions
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
More terms from John Mason, Oct 28 2023
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