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 A113848 #17 Feb 08 2015 14:20:16
%S A113848 1,1,3,11,127,16151,260855055,68045359719085327,
%T A113848 4630170979299719971778494028407039,
%U A113848 21438483297549327871400796194793048411084076762817293736211302918175
%N A113848 a(1) = a(2) = 1, a(n+2) = 2*a(n) + a(n+1)^2.
%C A113848 In this sequence the primes begin a(3) = 3, a(4) = 11, a(5) = 127, a(9) = 4630170979299719971778494028407039.
%H A113848 <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>
%F A113848 a(1) = a(2) = 1, for n>2: a(n) = 2*a(n-2) + a(n-1)^2. a(1) = a(2) = 1, for n>0: a(n+2) = 2*a(n) + a(n+1)^2.
%F A113848 a(n) ~ c^(2^n), where c = 1.163464453662702696843453679269882816346479873363677551158525103156732040997... . - _Vaclav Kotesovec_, Dec 18 2014
%e A113848 a(1) = 1 by definition.
%e A113848 a(2) = 1 by definition.
%e A113848 a(3) = 2*1 + 1^2 = 3.
%e A113848 a(4) = 2*1 + 3^2 = 11.
%e A113848 a(5) = 2*3 + 11^2 = 127.
%e A113848 a(6) = 2*11 + 127^2 = 16151.
%t A113848 Join[{a=1,b=1},Table[c=1*b^2+2*a;a=b;b=c,{n,10}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 18 2011 *)
%t A113848 RecurrenceTable[{a[1]==1, a[2]==1, a[n] == 2*a[n-2] + a[n-1]^2}, a, {n, 1, 10}] (* _Vaclav Kotesovec_, Dec 18 2014 *)
%Y A113848 Cf. A000278, A000283, A014253, A063827, A072878, A112957, A112958, A112959, A112960, A112961, A112969, A113785.
%K A113848 easy,nonn
%O A113848 1,3
%A A113848 _Jonathan Vos Post_, Jan 24 2006