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A369471
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Number of chiral pairs of polyominoes composed of n pentagonal cells of the hyperbolic regular tiling with Schläfli symbol {5,oo}.
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5
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4, 24, 172, 1144, 8056, 57800, 427006, 3221216, 24773668, 193592840, 1534006620, 12301987920, 99699269740, 815520435048, 6725987757744, 55882659600320, 467387108739408, 3932600291539096, 33269691987278258, 282863688830816184
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OFFSET
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4,1
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COMMENTS
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A stereographic projection of the {5,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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MATHEMATICA
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p=5; Table[(Binomial[(p-1)n, n]/(((p-2)n+1)((p-2)n+2))-If[OddQ[n], If[OddQ[p], Binomial[(p-1)n/2, (n-1)/2]/n, (p+1)Binomial[((p-1)n-1)/2, (n-1)/2]/((p-2)n+2)-Binomial[((p-1)n+1)/2, (n-1)/2]/((p-1)n+1)], Binomial[(p-1)n/2, n/2]/((p-2)n+2)]+DivisorSum[GCD[p, n-1], EulerPhi[#]Binomial[((p-1)n+1)/#, (n-1)/#]/((p-1)n+1)&, #>1&])/2, {n, 4, 30}]
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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