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A075869 5*n^2 - 9 is a square. 0
3, 51, 915, 16419, 294627, 5286867, 94868979, 1702354755, 30547516611, 548152944243, 9836205479763, 176503545691491, 3167227616967075, 56833593559715859, 1019837456457918387, 18300240622682815107 (list; graph; refs; listen; history; text; 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, pp. 341-400.

Peter G. L. Dirichlet, Lectures on Number Theory (History of Mathematics Source Series, V. 16); American Mathematical Society, Providence, Rhode Island, 1999, pp. 139-147.

LINKS

Table of n, a(n) for n=1..16.

Tanya Khovanova, Recursive Sequences

J. J. O'Connor and E. F. Robertson, Pell's Equation

Eric Weisstein's World of Mathematics, Pell Equation.

Index entries for linear recurrences with constant coefficients, signature (18,-1).

FORMULA

a(n) = 3*sqrt(5)/10*((2+sqrt(5))^(2*n-1)-(2-sqrt(5))^(2*n-1)) = 18*a(n-1) - a(n-2)

G.f.: 3x*(1-3x)/(1-18x+x^2). [From Philippe Deléham, Nov 17 2008]

CROSSREFS

Cf. 3*A007805.

Sequence in context: A248341 A145242 A182512 * A126685 A246693 A187666

Adjacent sequences:  A075866 A075867 A075868 * A075870 A075871 A075872

KEYWORD

nonn,easy

AUTHOR

Gregory V. Richardson, Oct 16 2002

STATUS

approved

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Last modified November 21 22:32 EST 2017. Contains 295054 sequences.