%I #13 Sep 05 2020 18:26:12
%S 0,1,2,9,40,77,342,1519,2924,12987,57682,111035,493164,2190397,
%T 4216406,18727245,83177404,160112393,711142146,3158550955,6080054528,
%U 27004674303,119941758886,230881959671,1025466481368,4554628286713
%N 40*n^2 + 9 is a square.
%C Lim. n-> Inf. a(n)/a(n-3) = 19 + 6*Sqrt(10). Lim. n-> Inf. a(3*k)/a(3*k-1) = (11 + 2*Sqrt(10))/9. Lim. n-> Inf. a(3*k+1)/a(3*k) = (7 + 2*Sqrt(10))/3. Lim. n-> Inf. a(3*k+2)/a(3*k+1) = (7 + 2*Sqrt(10))/3.
%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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PellEquation.html">Pell Equation.</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,38,0,0,-1)
%F G.f.: x^2*(x^5+2x^4+9x^3+2x^2+x)/(x^6-38x^3+1).
%F a(n) = A075836(n)/2.
%t LinearRecurrence[{0,0,38,0,0,-1},{0,1,2,9,40,77},30] (* _Harvey P. Dale_, Sep 05 2020 *)
%K nonn
%O 1,3
%A _Gregory V. Richardson_, Oct 16 2002
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