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 A195620 #22 Feb 16 2023 09:04:30
%S A195620 63,4161,274559,18116737,1195430079,78880268481,5204902289663,
%T A195620 343444670849281,22662143373762879,1495358017997500737,
%U A195620 98670967044461285759,6510788466916447359361,429613367849441064432063,28347971489596193805156801
%N A195620 Numerators of Pythagorean approximations to 4.
%C A195620 See A195500 for discussion and list of related sequences; see A195616 for Mathematica program.
%H A195620 Colin Barker, <a href="/A195620/b195620.txt">Table of n, a(n) for n = 1..549</a>
%H A195620 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (65,65,-1).
%F A195620 From _Colin Barker_, Jun 03 2015: (Start)
%F A195620 a(n) = 65*a(n-1) + 65*a(n-2) - a(n-3).
%F A195620 G.f.: x*(63+66*x-x^2) / ((1+x)*(1-66*x+x^2)). (End)
%F A195620 a(n) = ((-1)^n - 2*(-4+sqrt(17))*(33+8*sqrt(17))^(-n) + 2*(4+sqrt(17))*(33+8*sqrt(17))^n)/17. - _Colin Barker_, Mar 03 2016
%F A195620 a(n) = (1/17)*(A078989(n) + (-1)^n) - [n=0]. - _G. C. Greubel_, Feb 15 2023
%t A195620 LinearRecurrence[{65,65,-1}, {63,4161,274559}, 40] (* _G. C. Greubel_, Feb 15 2023 *)
%o A195620 (PARI) Vec(x*(63+66*x-x^2)/((1+x)*(1-66*x+x^2)) + O(x^20)) \\ _Colin Barker_, Jun 03 2015
%o A195620 (Magma) I:=[63,4161,274559]; [n le 3 select I[n] else 65*Self(n-1) +65*Self(n-2) -Self(n-3): n in [1..40]]; // _G. C. Greubel_, Feb 15 2023
%o A195620 (SageMath)
%o A195620 A078989=BinaryRecurrenceSequence(66, -1, 1, 67)
%o A195620 [(16*A078989(n) + (-1)^n)/17 for n in range(1, 41)] # _G. C. Greubel_, Feb 15 2023
%Y A195620 Cf. A078989, A195500, A195619, A195620.
%K A195620 nonn,easy
%O A195620 1,1
%A A195620 _Clark Kimberling_, Sep 22 2011