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 A342817 #9 Mar 23 2021 04:51:31
%S A342817 1,-4,4,16,52,112,-48,-1984,-11212,-33360,6224,713536,4441872,
%T A342817 13004480,-17374656,-432012032,-2525831628,-6454496208,21147389392,
%U A342817 326358047552,1794285832464,4124461926592,-19727734694848,-263598020446976,-1416694290412784,-3151402998261312
%N A342817 Power series expansion of AQM(1,1-8x) where AQM denotes the arithmetic-quadratic mean.
%C A342817 Generating function: AQM(1,1-8x) where AQM(u,v) (arithmetic-quadratic mean of u and v) is the fixed point obtained by iterating ((u+v)/2, sqrt((u^2+v^2)/2)) (we choose 1-8x in order to avoid denominators, as in A060691).
%e A342817 First steps of iteration of ((u+v)/2, sqrt((u^2+v^2)/2)) are (1, 1-8x), (1 - 4*x, 1 - 4*x + 8*x^2 + 32*x^3 + 96*x^4 + O(x^5)), then (1 - 4*x + 4*x^2 + 16*x^3 + 48*x^4 + O(x^5), 1 - 4*x + 4*x^2 + 16*x^3 + 56*x^4 + O(x^5)) and (1 - 4*x + 4*x^2 + 16*x^3 + 52*x^4 + O(x^5), 1 - 4*x + 4*x^2 + 16*x^3 + 52*x^4 + O(x^5)), so the first terms of this sequence are 1, -4, 4, 16, 52.
%o A342817 (Sage)
%o A342817 R.<x> = PowerSeriesRing(QQ, default_prec=50)
%o A342817 (a,b) = (1,1-8*x)
%o A342817 for i in range(50):
%o A342817 (a,b) = ((a+b)/2, sqrt((a^2+b^2)/2))
%o A342817 a.coefficients()
%o A342817 (PARI) seq(n)={my(p=1, q=1-8*x+O(x*x^n)); while(p!=q, my(t=p+q); q = sqrt((p^2 + q^2)/2); p=t/2); Vec(p)} \\ _Andrew Howroyd_, Mar 22 2021
%Y A342817 Compare A060691 for the arithmetic-geometric mean.
%K A342817 sign
%O A342817 0,2
%A A342817 _David A. Madore_, Mar 22 2021