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A054887
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Layer counting sequence for hyperbolic tessellation by cuspidal triangles of angles (Pi/3, Pi/5, Pi/7).
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4
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1, 3, 6, 11, 20, 36, 64, 113, 200, 354, 626, 1107, 1958, 3464, 6128, 10839, 19172, 33913, 59988, 106111, 187696, 332009, 587280, 1038820, 1837534, 3250353, 5749442, 10169998, 17989372, 31820803, 56286764, 99563792, 176115092
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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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Index entries for linear recurrences with constant coefficients, signature (0,0,2,2,4,3,4,2,2,0,0,-1).
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FORMULA
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G.f.: x*(1+x)*(1-x^3)*(1-x^5)*(1-x^7)/(1-2*x+x^4+x^6-x^10-x^12+2*x^15-x^16).
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MATHEMATICA
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LinearRecurrence[{0, 0, 2, 2, 4, 3, 4, 2, 2, 0, 0, -1}, {1, 3, 6, 11, 20, 36, 64, 113, 200, 354, 626, 1107, 1958}, 41] (* G. C. Greubel, Feb 07 2023 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x*(1+x)*(1-x^3)*(1-x^5)*(1-x^7)/(1-2*x+x^4+x^6-x^10-x^12+2*x^15-x^16) )); // G. C. Greubel, Feb 07 2023
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(1+x)*(1-x^3)*(1-x^5)*(1-x^7)/(1-2*x+x^4+x^6-x^10-x^12+2*x^15-x^16) ).list()
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
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STATUS
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approved
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