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A005038
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Number of nonequivalent dissections of a polygon into n pentagons by nonintersecting diagonals up to rotation.
(Formerly M2026)
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11
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1, 1, 2, 12, 57, 366, 2340, 16252, 115940, 854981, 6444826, 49554420, 387203390, 3068067060, 24604111560, 199398960212, 1631041938108, 13451978877748, 111765327780200, 934774244822704, 7865200653146905
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OFFSET
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1,3
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COMMENTS
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Also, with a different offset, number of colored quivers in the 3-mutation class of a quiver of Dynkin type A_n. - N. J. A. Sloane, Jan 22 2013
Number of oriented polyominoes composed of n pentagonal cells of the hyperbolic regular tiling with Schläfli symbol {5,oo}. A stereographic projection of this tiling on the Poincaré disk can be obtained via the Christensson link. For oriented polyominoes, chiral pairs are counted as two. - Robert A. Russell, Jan 23 2024
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) ~ 2^(8*n + 1/2) / (sqrt(Pi) * n^(5/2) * 3^(3*n + 5/2)). - Vaclav Kotesovec, Mar 13 2016
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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], 0, Binomial[(p-1)n/2, n/2]/((p-2)n+2)]+Plus @@ Map[EulerPhi[ # ]Binomial[((p-1)n+1)/#, (n-1)/# ]/((p-1)n+1)&, Complement[Divisors[GCD[p, n-1]], {1}]], {n, 1, 20}] (* Robert A. Russell, Dec 11 2004 *)
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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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EXTENSIONS
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STATUS
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approved
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