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%I #24 Feb 02 2020 04:06:28
%S 1,1,59,60,3539,3599,212281,215880,12733321,12949201,763786979,
%T 776736180,45814485419,46591221599,2748105338161,2794696559760,
%U 164840505804241,167635202364001,9887682242916299,10055317445280300,593096094069173699
%N Denominators of continued fraction convergents to sqrt(899).
%C The following remarks assume an offset of 1. This is the sequence of Lehmer numbers U_n(sqrt(R),Q) for the parameters R = 58 and Q = -1. This is a strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for all positive integers n and m. Consequently, this is a divisibility sequence: if n divides m then a(n) divides a(m). - _Peter Bala_, May 26 2014
%H Vincenzo Librandi, <a href="/A042739/b042739.txt">Table of n, a(n) for n = 0..200</a>
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/LehmerNumber.html">MathWorld: Lehmer Number</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,60,0,-1).
%F G.f.: -(x^2-x-1) / (x^4-60*x^2+1). - _Colin Barker_, Dec 22 2013
%F From _Peter Bala_, May 26 2014: (Start)
%F The following remarks assume an offset of 1. Let alpha = ( sqrt(58) + sqrt(62) )/2 and beta = ( sqrt(58) - sqrt(62) )/2 be the roots of the equation x^2 - sqrt(58)*x - 1 = 0.
%F Then a(n) = (alpha^n - beta^n)/(alpha - beta) for n odd, while
%F a(n) = (alpha^n - beta^n)/(alpha^2 - beta^2) for n even.
%F a(n) = product {k = 1..floor((n-1)/2)} (58 + 4*cos^2(k*Pi/n)).
%F Recurrence equations: a(0) = 0, a(1) = 1 and for n >= 1, a(2*n) = a(2*n - 1) + a(2*n - 2) and a(2*n + 1) = 58*a(2*n) + a(2*n - 1). (End)
%t Denominator[Convergents[Sqrt[899], 30]] (* _Vincenzo Librandi_, Jan 28 2014 *)
%t LinearRecurrence[{0,60,0,-1},{1,1,59,60},30] (* _Harvey P. Dale_, Apr 01 2017 *)
%Y Cf. A042738, A040869. A002530.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E Additional term from _Colin Barker_, Dec 22 2013
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