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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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Index entries for sequences related to linear recurrences with constant coefficients
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)
G.f.: 3x(1-x)/(1-6x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 17 2008]
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CROSSREFS
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Sequence in context: A127085 A093615 A001931 this_sequence A152596 A089022 A132371
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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