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%I #34 Dec 29 2020 20:39:29
%S 0,6,36,210,1224,7134,41580,242346,1412496,8232630,47983284,279667074,
%T 1630019160,9500447886,55372668156,322735561050,1881040698144,
%U 10963508627814,63900011068740,372436557784626,2170719335639016
%N Numbers k such that 2*k^2 + 9 is a square.
%C Lim_{n->infinity} a(n)/a(n-1) = 3 + 2*sqrt(2).
%D 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.
%D L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, pp. 341-400.
%D 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.
%H Harvey P. Dale, <a href="/A075848/b075848.txt">Table of n, a(n) for n = 0..1000</a>
%H Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Nemeth/nemeth7.html">Ellipse Chains and Associated Sequences</a>, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H J. J. O'Connor and E. F. Robertson, <a href="http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Pell.html">Pell's Equation</a>
%H Soumeya M. Tebtoub, Hacène Belbachir, and László Németh, <a href="https://hal.archives-ouvertes.fr/hal-02918958/document#page=18">Integer sequences and ellipse chains inside a hyperbola</a>, Proceedings of the 1st International Conference on Algebras, Graphs and Ordered Sets (ALGOS 2020), hal-02918958 [math.cs], 17-18.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PellEquation.html">Pell Equation.</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-1).
%F a(n) = ((3+2*sqrt(2))^n - (3-2*sqrt(2))^n) * (3/(2*sqrt(2)));
%F a(n) = 6*a(n-1) - a(n-2).
%F a(n) = 6*A001109(n).
%F G.f.: 6x/(1-6x+x^2). - _Philippe Deléham_, Nov 17 2008
%t LinearRecurrence[{6,-1},{0,6},30] (* _Harvey P. Dale_, Nov 28 2012 *)
%K nonn,easy
%O 0,2
%A _Gregory V. Richardson_, Oct 15 2002
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