This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A041683 #26 Feb 16 2025 08:32:38
%S A041683 1,1,37,38,1405,1443,53353,54796,2026009,2080805,76934989,79015794,
%T A041683 2921503573,3000519367,110940200785,113940720152,4212806126257,
%U A041683 4326746846409,159975692596981,164302439443390,6074863512559021,6239165952002411
%N A041683 Denominators of continued fraction convergents to sqrt(360).
%C A041683 The following remarks assume an offset of 1. This is the sequence of Lehmer numbers U_n(sqrt(R),Q) for the parameters R = 36 and Q = -1; it 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 28 2014
%H A041683 Vincenzo Librandi, <a href="/A041683/b041683.txt">Table of n, a(n) for n = 0..200</a>
%H A041683 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/LehmerNumber.html">MathWorld: Lehmer Number</a>
%H A041683 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,38,0,-1).
%F A041683 G.f.: -(x^2-x-1) / ((x^2-6*x-1)*(x^2+6*x-1)). - _Colin Barker_, Nov 21 2013
%F A041683 a(n) = 38*a(n-2) - a(n-4) for n > 3. - _Vincenzo Librandi_, Dec 22 2013
%F A041683 From _Peter Bala_, May 28 2014: (Start)
%F A041683 The following remarks assume an offset of 1.
%F A041683 Let alpha = 3 + sqrt(10) and beta = 3 - sqrt(10) be the roots of the equation x^2 - 6*x - 1 = 0. Then a(n) = (alpha^n - beta^n)/(alpha - beta) for n odd, while a(n) = (alpha^n - beta^n)/(alpha^2 - beta^2) for n even.
%F A041683 a(n) = A005668(n+1) for n even; a(n) = 1/6*A005668(n+1) for n odd.
%F A041683 a(n) = Product_{k = 1..floor((n-1)/2)} ( 36 + 4*cos^2(k*Pi/n) ).
%F A041683 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) = 36*a(2*n) + a(2*n - 1). (End)
%t A041683 Denominator[Convergents[Sqrt[360], 30]] (* _Vincenzo Librandi_, Dec 22 2013 *)
%o A041683 (Magma) I:=[1,1,37,38]; [n le 4 select I[n] else 38*Self(n-2)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Dec 22 2013
%Y A041683 Cf. A041682, A040341, A002530, A005668.
%K A041683 nonn,frac,easy
%O A041683 0,3
%A A041683 _N. J. A. Sloane_
%E A041683 More terms from _Colin Barker_, Nov 21 2013