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A088920
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Solutions k to the Diophantine equation k = 2n^2 = m^2+1.
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1
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2, 50, 1682, 57122, 1940450, 65918162, 2239277042, 76069501250, 2584123765442, 87784138523762, 2982076586042450, 101302819786919522, 3441313796169221282, 116903366249966604050, 3971273138702695316402
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| Eric Weisstein's World of Mathematics, NSW Number
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FORMULA
| G.f.: (2x^2-20x+2)/[(1-x)(1-34x+x^2)].
a(n) = -(Sinh[(2 n - 1) ArcTanh[Sqrt[2]]])^2 = 1 -(Cosh[(2 n - 1) ArcTanh[Sqrt[2]]])^2 [From Artur Jasinski (grafix(AT)csl.pl), Oct 30 2008]
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MATHEMATICA
| Table[Round[N[ -(Sinh[(2 n - 1) ArcTanh[Sqrt[2]]])^2, 100]], {n, 1, 20}] [From Artur Jasinski (grafix(AT)csl.pl), Oct 30 2008]
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CROSSREFS
| Corresponding solutions of n are A001653 and m are A002315.
A008843(n-1) + 1.
Sequence in context: A083939 A083941 A080263 * A079198 A203766 A197487
Adjacent sequences: A088917 A088918 A088919 * A088921 A088922 A088923
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Oct 23, 2003
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