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 A284604 #14 Feb 16 2025 11:37:33
%S A284604 1,1,3,11,131,17283,298719251,89233191216703091,
%T A284604 7962562414716697755180182566955283,
%U A284604 63402400208259008611705446682872670539115181497111590988296570564371
%N A284604 Quadratic recurrence: a(n+2) = a(n+1)^2 + a(n)^2 + 1, with a(0) = a(1) = 1.
%F A284604 a(n+3) = a(n+2)^2 + a(n+2) - a(n)^2, with a(0) = a(1) = 1, a(2) = 3.
%F A284604 a(n) ~ c^(2^n), where c = 1.356519333072951374233963037913978335267300244021120535099185060013... - _Vaclav Kotesovec_, Apr 15 2017
%t A284604 RecurrenceTable[{a[n + 2] == a[n + 1]^2 + a[n]^2 + 1, a[0] == 1, a[1] == 1}, a, {n, 0, 12}]
%t A284604 nxt[{a_,b_}]:={b,a^2+b^2+1}; NestList[nxt,{1,1},10][[;;,1]] (* _Harvey P. Dale_, Feb 16 2025 *)
%o A284604 (Maxima) a(n) := if (n=0 or n=1) then 1 else a(n-1)^2 + a(n-2)^2 + 1; makelist(a(n), n, 0, 12);
%o A284604 (Magma) [n le 2 select 1 else Self(n-1)^2+Self(n-2)^2+1: n in [1..10]]; // _Bruno Berselli_, Mar 30 2017
%Y A284604 Cf. A000283.
%K A284604 nonn
%O A284604 0,3
%A A284604 _Emanuele Munarini_, Mar 30 2017