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A054889
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Layer counting sequence for hyperbolic tessellation by regular pentagons of angle 2*Pi/5.
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3
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1, 5, 20, 70, 245, 860, 3015, 10570, 37060, 129935, 455560, 1597225, 5599980, 19633910, 68837825, 241350100, 846189875, 2966799290, 10401800220, 36469419475, 127864266640, 448300820765, 1571773187140, 5510743762630
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OFFSET
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1,2
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COMMENTS
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The layer sequence is the sequence of the cardinalities of the layers accumulating around a (finite-sided) polygon of the tessellation under successive side-reflections; see the illustration accompanying A054888.
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LINKS
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FORMULA
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G.f.: x*(1+2*x+4*x^2+2*x^3+x^4)/(1-3*x-x^2-3*x^3+x^4).
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MATHEMATICA
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LinearRecurrence[{3, 1, 3, -1}, {1, 5, 20, 70, 245}, 40] (* Georg Fischer, Apr 13 2020 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x*(1+2*x+4*x^2+2*x^3+x^4)/(1-3*x-x^2-3*x^3+x^4) )); // G. C. Greubel, Feb 08 2023
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(1+2*x+4*x^2+2*x^3+x^4)/(1-3*x-x^2-3*x^3+x^4) ).list()
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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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Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
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EXTENSIONS
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STATUS
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approved
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