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A075848
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2*n^2 + 9 is a square.
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Lim. n-> Inf. a(n)/a(n-1) = 3 + 2*Sqrt(2).
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REFERENCES
| 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
| 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, Pell Equation.
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FORMULA
| 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)
G.f.: 6x/(1-6x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 17 2008]
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CROSSREFS
| Sequence in context: A064238 A014336 A027910 * A096979 A123887 A105492
Adjacent sequences: A075845 A075846 A075847 * A075849 A075850 A075851
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KEYWORD
| nonn
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AUTHOR
| Gregory V. Richardson (omomom(AT)hotmail.com), Oct 15 2002
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