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Search: id:A075848
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| 0, 6, 36, 210, 1224, 7134, 41580, 242346, 1412496, 8232630, 47983284, 279667074, 1630019160, 9500447886, 55372668156, 322735561050, 1881040698144, 10963508627814, 63900011068740, 372436557784626, 2170719335639016
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OFFSET
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0,2
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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+2*Sqrt(2))^n - (3-2*Sqrt(2))^n] * [3/(2*Sqrt(2))]; a(n) = 6*a(n-1) - a(n-2); a(n) = 6 * (A001109)
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CROSSREFS
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Sequence in context: A064238 A014336 A027910 this_sequence A096979 A123887 A105492
Adjacent sequences: A075845 A075846 A075847 this_sequence A075849 A075850 A075851
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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 15 2002
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