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Search: id:A075841
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| 3, 15, 87, 507, 2955, 17223, 100383, 585075, 3410067, 19875327, 115841895, 675176043, 3935214363, 22936110135, 133681446447, 779152568547, 4541233964835, 26468251220463, 154268273357943, 899141388927195
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OFFSET
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1,1
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COMMENT
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Lim. n-> Inf. a(n)/a(n-1) = 3 + 2*Sqrt(2).
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REFERENCES
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A. H. Beiler, "The Pellian", ch. 22 in Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. Dover, New York, New York, pp. 248-268, 1966.
L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, p. 341-400.
Peter G. L. Dirichlet, Lectures on Number Theory (History of Mathematics Source Series, V. 16); American Mathematical Society, Providence, Rhode Island, 1999, p. 139-147.
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LINKS
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Tanya Khovanova, Recursive Sequences
J. J. O'Connor and E. F. Robertson, Pell's Equation
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n) = 3*sqrt(2)/4*((1+sqrt(2))^(2*n-1)-(1-sqrt(2))^(2*n-1)) = 6*a(n-1) - a(n-2)
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CROSSREFS
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Sequence in context: A127085 A093615 A001931 this_sequence A089022 A132371 A127785
Adjacent sequences: A075838 A075839 A075840 this_sequence A075842 A075843 A075844
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KEYWORD
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nonn
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AUTHOR
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Gregory V. Richardson (omomom(AT)hotmail.com), Oct 14 2002
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