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A091648
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Decimal expansion of arccosh(sqrt(2)), the inflection point of sech(x).
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7
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8, 8, 1, 3, 7, 3, 5, 8, 7, 0, 1, 9, 5, 4, 3, 0, 2, 5, 2, 3, 2, 6, 0, 9, 3, 2, 4, 9, 7, 9, 7, 9, 2, 3, 0, 9, 0, 2, 8, 1, 6, 0, 3, 2, 8, 2, 6, 1, 6, 3, 5, 4, 1, 0, 7, 5, 3, 2, 9, 5, 6, 0, 8, 6, 5, 3, 3, 7, 7, 1, 8, 4, 2, 2, 2, 0, 2, 6, 0, 8, 7, 8, 3, 3, 7, 0, 6, 8, 9, 1, 9, 1, 0, 2, 5, 6, 0, 4, 2, 8, 5, 6
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Asymptotic growth constant in the exponent for the number of spanning trees on the 2 X infinity strip on the square lattice. - R. J. Mathar, May 14 2006
Equals sum({n>=1, n odd} binomial(2*n,n)/(n*4^n) [D. H. Lehmer, Am. Math. Monthly 92 (1985) 449] [From R. J. Mathar, Mar 04 2009]
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REFERENCES
| Jolley, Summation of Series, Dover (1961), eq (85) page 16.
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LINKS
| Eric Weisstein's World of Mathematics, Hyperbolic Secant
Eric Weisstein's World of Mathematics, Universal Parabolic Constant
R. Shrock and F. Y. Wu, Spanning trees on graphs and lattices in d dimensions, J Phys A: Math Gen 33 (2000) 3881-3902
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FORMULA
| ln(1 + sqrt(2)) - Jonathan Sondow, Mar 15 2005
(1/2)*ln(3+2*sqrt(2)) - R. J. Mathar, May 14 2006
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EXAMPLE
| 0.88137358...
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MATHEMATICA
| RealDigits[Log[1 + Sqrt[2]], 10, 100][[1]] (* From Alonso del Arte, Aug 11 2011 *)
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CROSSREFS
| Cf. A103710, A103711, A103712, A181048.
Sequence in context: A141134 A176155 A174127 * A135707 A021923 A065465
Adjacent sequences: A091645 A091646 A091647 * A091649 A091650 A091651
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KEYWORD
| nonn,cons,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Jan 24 2004
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