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 A165896 #19 Aug 21 2016 11:07:47
%S A165896 1,1,1,1,6,51,3001,9180001,14050074147451,3870680638643416483474006,
%T A165896 4992392071450646411005278674572370014340582601,
%U A165896 2715030052293379508289500941366397276374058263752394148988972928520177978202810359001
%N A165896 a(n) = (a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-1)*a(n-2)+a(n-1)*a(n-3)+a(n-2)*a(n-3))/a(n-4) with four initial ones.
%H A165896 Seiichi Manyama, <a href="/A165896/b165896.txt">Table of n, a(n) for n = 0..15</a>
%H A165896 S. Fomin, A. Zelevinsky, <a href="http://dx.doi.org/10.1006/aama.2001.0770">The Laurent Phenomenon</a>, Adv. Appl. Math. 28 (2) (2002) 119-144. [_R. J. Mathar_, Oct 23 2009]
%H A165896 Sergey Fomin, Andrei Zelevinsky, <a href="http://arxiv.org/abs/math/0104241">The Laurent phenomenon</a>, arXiv:math/0104241 [math.CO], 2001. [_R. J. Mathar_, Oct 23 2009]
%F A165896 a(n) ~ 1/sqrt(10) * c^(t^n), where t = A058265 = 1.8392867552141611325518525646532866..., c = 1.2712241060822553131735186905646486868228186258439... . - _Vaclav Kotesovec_, May 06 2015
%F A165896 a(n) = 10*a(n-1)*a(n-2)*a(n-3)-a(n-1)-a(n-2)-a(n-3)-a(n-4). - _Bruno Langlois_, Aug 21 2016
%t A165896 RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==1,a[n]==(a[n-1]^2+a[n-2]^2+a[n-3]^2+ a[n-1]a[n-2]+ a[n-1]a[n-3]+a[n-2]a[n-3])/a[n-4]},a,{n,13}] (* _Harvey P. Dale_, May 21 2012 *)
%o A165896 (PARI) a(n)=if(n<4,1,(a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-1)*a(n-2)+a(n-1)*a(n-3)+a(n-2)*a(n-3))/a(n-4))
%Y A165896 Cf. A006720, A165903.
%K A165896 nonn
%O A165896 0,5
%A A165896 _Jaume Oliver Lafont_, Sep 29 2009