A075869 - OEIS

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A075869

5*n^2 - 9 is a square.

3, 51, 915, 16419, 294627, 5286867, 94868979, 1702354755, 30547516611, 548152944243, 9836205479763, 176503545691491, 3167227616967075, 56833593559715859, 1019837456457918387, 18300240622682815107 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	COMMENTS	`Lim. n-> Inf. a(n)/a(n-1) = phi^6 = 9 + 4*Sqrt(5).`
	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	`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.`
	FORMULA	`a(n) = 3sqrt(5)/10((2+sqrt(5))^(2n-1)-(2-sqrt(5))^(2n-1)) = 18a(n-1) - a(n-2)` `G.f.: 3x(1-3x)/(1-18x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 17 2008]`
	CROSSREFS	`Cf. 3A007805.` `Sequence in context: A116630 A045489 A145242 A126685 A187666 A172434` `Adjacent sequences: A075866 A075867 A075868 * A075870 A075871 A075872`
	KEYWORD	`nonn`
	AUTHOR	`Gregory V. Richardson (omomom(AT)hotmail.com), Oct 16 2002`

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Last modified February 17 04:58 EST 2012. Contains 205985 sequences.