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 A195549 #30 May 11 2022 10:29:48 %S A195549 1,5,13,17,89,233,305,1597,4181,5473,28657,75025,98209,514229,1346269, %T A195549 1762289,9227465,24157817,31622993,165580141,433494437,567451585, %U A195549 2971215073,7778742049,10182505537,53316291173,139583862445,182717648081 %N A195549 Hypotenuses of primitive Pythagorean triples in A195547 and A195548. %C A195549 See A195500 for discussion and list of related sequences; see A195547 for Mathematica program. %F A195549 a(n) = (F(n)^2 + F(n+1)^2)/(2 - ((n+2)^2 mod 3)), F(n) = Fibonacci(n). - _Gary Detlefs_, Oct 14 2011 %F A195549 Conjectures from _Colin Barker_, Apr 08 2012: (Start) %F A195549 a(n) = 18*a(n-3) - a(n-6). %F A195549 G.f.: x*(1+5*x+13*x^2-x^3-x^4-x^5)/((1-3*x+x^2)*(1+3*x+8*x^2+3*x^3+x^4)). (End) %F A195549 Conjecture: a(n) is the denominator of the reduced fraction (F(2*n+1)-2)/F(2*n+1), F(n) = Fibonacci(n). - _Sébastien Labbé_, May 06 2022 %p A195549 with(combinat):f:= n-> fibonacci(n):seq((f(n)^2+f(n+1)^2)/(2-((n+2)^2 mod 3)), n=1..25); %Y A195549 Cf. A000045, A195500, A195547, A195548, A131534. %K A195549 nonn %O A195549 1,2 %A A195549 _Clark Kimberling_, Sep 20 2011