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 A041479 #27 Feb 16 2025 08:32:38
%S A041479 1,1,31,32,991,1023,31681,32704,1012801,1045505,32377951,33423456,
%T A041479 1035081631,1068505087,33090234241,34158739328,1057852414081,
%U A041479 1092011153409,33818187016351,34910198169760
%N A041479 Denominators of continued fraction convergents to sqrt(255).
%C A041479 The following remarks assume an offset of 1. This is the sequence of Lehmer numbers U_n(sqrt(R),Q) for the parameters R = 30 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 A041479 Vincenzo Librandi, <a href="/A041479/b041479.txt">Table of n, a(n) for n = 0..200</a>
%H A041479 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/LehmerNumber.html">MathWorld: Lehmer Number</a>
%H A041479 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,32,0,-1).
%F A041479 From _Colin Barker_, Jul 16 2012: (Start)
%F A041479 a(n) = 32*a(n-2) - a(n-4).
%F A041479 G.f.: -(x^2-x-1)/(x^4-32*x^2+1). (End)
%F A041479 From _Peter Bala_, May 28 2014: (Start)
%F A041479 The following remarks assume an offset of 1.
%F A041479 Let alpha = ( sqrt(30) + sqrt(34) )/2 and beta = ( sqrt(30) - sqrt(34) )/2 be the roots of the equation x^2 - sqrt(30)*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 A041479 a(n) = Product_{k = 1..floor((n-1)/2)} ( 30 + 4*cos^2(k*Pi/n) ).
%F A041479 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) = 30*a(2*n) + a(2*n - 1). (End)
%t A041479 Denominator[Convergents[Sqrt[255],30]] (* or *) LinearRecurrence[ {0,32,0,-1},{1,1,31,32},30] (* _Harvey P. Dale_, Jan 19 2013 *)
%t A041479 CoefficientList[Series[- (x^2 - x - 1)/(x^4 - 32 x^2 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 25 2013 *)
%Y A041479 Cf. A041478, A176110, A002530.
%K A041479 nonn,cofr,frac,easy
%O A041479 0,3
%A A041479 _N. J. A. Sloane_