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Search: id:A091648
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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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+0
5
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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; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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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 (mathar(AT)strw.leidenuniv.nl), May 14 2006
Equals sum_{n=1..infinity, n odd} binomial(2n,n)/(n*4^n) [D. H. Lehmer, Am. Math. Monthly 92 (1985) 449] [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 04 2009]
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LINKS
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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
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ln(1 + sqrt(2)) - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Mar 15 2005
(1/2)*ln(3+2*sqrt(2)) - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 14 2006
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EXAMPLE
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0.88137358...
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CROSSREFS
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Cf. A103710, A103711, A103712.
Sequence in context: A056194 A110940 A141134 this_sequence A135707 A021923 A065465
Adjacent sequences: A091645 A091646 A091647 this_sequence A091649 A091650 A091651
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KEYWORD
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nonn,cons,easy
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Jan 24, 2004
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