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A054890
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Layer counting sequence for hyperbolic tessellation by regular heptagons of angle Pi/3.
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3
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1, 7, 42, 245, 1428, 8323, 48510, 282737, 1647912, 9604735, 55980498, 326278253, 1901689020, 11083855867, 64601446182, 376524821225, 2194547481168, 12790760065783, 74550012913530, 434509317415397
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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+x+x^2)/(1-6*x+x^2).
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MATHEMATICA
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Rest@CoefficientList[Series[x*(1+x+x^2)/(1-6*x+x^2), {x, 0, 30}], x] (* Michael De Vlieger, Dec 29 2020 *)
LinearRecurrence[{6, -1}, {1, 7, 42}, 20] (* Harvey P. Dale, Jun 06 2021 *)
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PROG
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(Magma) [n eq 1 select 1 else 7*Evaluate(ChebyshevSecond(n-1), 3): n in [1..40]]; // G. C. Greubel, Feb 08 2023
(SageMath) [7*chebyshev_U(n-2, 3) + int(n==1) for n in range(1, 41)] # G. C. Greubel, Feb 08 2023
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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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