

A006534


Number of onesided triangular polyominoes (niamonds) with n cells; turning over not allowed, holes are allowed.
(Formerly M3287)


7



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
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OFFSET

1,4


COMMENTS

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


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.
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.


EXAMPLE

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)


CROSSREFS



KEYWORD

nonn,hard,nice


AUTHOR



EXTENSIONS



STATUS

approved



