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A075848 2*n^2 + 9 is a square. +0
3
0, 6, 36, 210, 1224, 7134, 41580, 242346, 1412496, 8232630, 47983284, 279667074, 1630019160, 9500447886, 55372668156, 322735561050, 1881040698144, 10963508627814, 63900011068740, 372436557784626, 2170719335639016 (list; graph; listen)
OFFSET

0,2

COMMENT

Lim. n-> Inf. a(n)/a(n-1) = 3 + 2*Sqrt(2).

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.

LINKS

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.

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)

CROSSREFS

Sequence in context: A064238 A014336 A027910 this_sequence A096979 A123887 A105492

Adjacent sequences: A075845 A075846 A075847 this_sequence A075849 A075850 A075851

KEYWORD

nonn

AUTHOR

Gregory V. Richardson (omomom(AT)hotmail.com), Oct 15 2002

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Last modified September 7 23:08 EDT 2008. Contains 143486 sequences.


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