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A097469
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Decimal expansion of growth constant C for dimer model on square grid.
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5
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1, 3, 3, 8, 5, 1, 5, 1, 5, 1, 9, 7, 6, 0, 9, 6, 7, 6, 6, 9, 3, 8, 1, 9, 5, 9, 0, 2, 0, 1, 8, 5, 1, 3, 5, 3, 7, 0, 6, 4, 3, 5, 3, 6, 9, 7, 1, 2, 7, 9, 1, 1, 3, 1, 4, 6, 4, 1, 2, 3, 4, 7, 8, 6, 6, 2, 2, 3, 9, 1, 1, 3, 3, 0, 0, 7, 9, 8, 0, 9, 7, 8, 6, 4, 6, 4, 8, 7, 3, 8, 4, 6, 1, 7, 7, 4, 4
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OFFSET
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1,2
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LINKS
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F. Ardila and R. P. Stanley, Tilings, arXiv:math/0501170 [math.CO], 2005.
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FORMULA
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Equals e^(G/Pi), with G = A006752 (Catalan's constant).
Equals exp((1/Pi^2) * Integral_{x=0..Pi/2, y=0..Pi/2} log(4*cos(x)^2 + 4*cos(y)^2) dx dy). - Vaclav Kotesovec, Jan 04 2021
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EXAMPLE
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1.33851515197609676693819590201851353706435369712791131464123...
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MATHEMATICA
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RealDigits[Exp[Catalan/Pi], 10, 100][[1]] (* G. C. Greubel, Aug 25 2018 *)
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PROG
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(PARI) default(realprecision, 100); exp(Catalan/Pi) \\ G. C. Greubel, Aug 25 2018
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); Exp(Catalan(R)/Pi(R)); // G. C. Greubel, Aug 25 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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