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 A195623 #24 Aug 05 2024 20:35:55
%S A195623 99,10101,1030199,105070201,10716130299,1092940220301,111469186340399,
%T A195623 11368764066500401,1159502465596700499,118257882726796950501,
%U A195623 12061144535667692250599,1230118484755377812610601,125460024300512869194030699,12795692360167557279978520701,1305035160712790329688615080799
%N A195623 Numerators of Pythagorean approximations to 5.
%C A195623 See A195500 for discussion and list of related sequences; see A195622 for Mathematica program.
%H A195623 Colin Barker, <a href="/A195623/b195623.txt">Table of n, a(n) for n = 1..497</a>
%H A195623 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (101,101,-1).
%F A195623 From _Colin Barker_, Jun 03 2015: (Start)
%F A195623 a(n) = 101*a(n-1) + 101*a(n-2) - a(n-3).
%F A195623 G.f.: x*(99+102*x-x^2)/((1+x)*(1-102*x+x^2)). (End)
%F A195623 a(n) = (1/26)*(25*A097726(n) + (-1)^n). - _G. C. Greubel_, Feb 16 2023
%F A195623 E.g.f.: (5*exp(51*x)*(5*cosh(10*sqrt(26)*x) + sqrt(26)*sinh(10*sqrt(26)*x)) + exp(-x) - 26)/26. - _Stefano Spezia_, Aug 05 2024
%t A195623 Table[(5*LucasL[2*n+1,10] +2*(-1)^n)/52, {n,40}] (* _G. C. Greubel_, Feb 16 2023 *)
%o A195623 (PARI) Vec(-x*(x^2-102*x-99) / ((x+1)*(x^2-102*x+1)) + O(x^20)) \\ _Colin Barker_, Jun 03 2015
%o A195623 (Magma) I:=[99,10101,1030199]; [n le 3 select I[n] else 101*Self(n-1) +101*Self(n-2) -Self(n-3): n in [1..40]]; // _G. C. Greubel_, Feb 16 2023
%o A195623 (SageMath)
%o A195623 A097726=BinaryRecurrenceSequence(102, -1, 1, 103)
%o A195623 [(1/26)*(25*A097726(n) + (-1)^n) for n in range(1, 41)] # _G. C. Greubel_, Feb 16 2023
%Y A195623 Cf. A097726, A097727, A195500, A195622.
%K A195623 nonn,easy,frac
%O A195623 1,1
%A A195623 _Clark Kimberling_, Sep 22 2011