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A369314
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Number of chiral pairs of polyominoes composed of n triangular cells of the hyperbolic regular tiling with Schläfli symbol {3,oo}.
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6
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1, 2, 7, 22, 68, 214, 691, 2240, 7396, 24702, 83469, 284928, 981814, 3410990, 11939752, 42075308, 149180356, 531866972, 1905872189, 6861162880, 24805796984, 90035940942, 327988261992, 1198853954688, 4395798528850
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OFFSET
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4,2
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COMMENTS
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A stereographic projection of the {3,oo} tiling on the Poincaré disk can be obtained via the Christensson link. Each member of a chiral pair is a reflection but not a rotation of the other.
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LINKS
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FORMULA
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a(n) = C(2n,2)/(2(n+1)(n+2)) - [2\(n+1)]*C(n,(n+1)/2)/(2n) - [2\n]*C(n,n/2)/(2n+4) + [3\(n-1)]*C((2n+1)/3,(n-1)/3)/(2n+1).
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EXAMPLE
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________ ________ ________ ________ ________ ________
\ /\ /\ /\ /\ / \ /\ /\ /\ /\ / \ /\ /\ /\ /\ /
\/__\/__\ /__\/__\/ \/__\/__\ /__\/__\/ \/__\/__\ /__\/__\/
\ / \ / \ / \ /
a(4)=1; a(5)=2. \/ \/ \/ \/
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MATHEMATICA
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Table[Binomial[2n, n]/(2(n+1)(n+2))-If[OddQ[n], Binomial[n, (n+1)/2]/n, Binomial[n, n/2]/(n+2)]/2+If[Divisible[n-1, 3], Binomial[(2n+1)/3, (n-1)/3]/(2n+1), 0], {n, 4, 20}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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