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A276271 a(0) = a(1) = a(2) = a(3) = 1; for n > 3, a(n) = (a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-1)+a(n-2)+a(n-3))/a(n-4).

%I A276271 #17 Oct 24 2018 08:07:18
%S A276271 1,1,1,1,6,46,2206,4870846,3954191749561,339905052007042640998641,
%T A276271 52373274877565894156748130733610185904753361,
%U A276271 563138297002425210235477817802336090254190075906443582099838858026136728896536841
%N A276271 a(0) = a(1) = a(2) = a(3) = 1; for n > 3, a(n) = (a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-1)+a(n-2)+a(n-3))/a(n-4).
%H A276271 Seiichi Manyama, <a href="/A276271/b276271.txt">Table of n, a(n) for n = 0..15</a>
%F A276271 a(n) = 8*a(n-1)*a(n-2)*a(n-3)-a(n-4)-1.
%F A276271 a(n) ~ 2^(-3/2) * c^(d^n), where c = 1.2578918597... and d = A058265 = 1.83928675521416... = (1 + (19 + 3*sqrt(33))^(1/3) + (19 - 3*sqrt(33))^(1/3))/3. - _Vaclav Kotesovec_, Mar 20 2017
%t A276271 nxt[{a_,b_,c_,d_}]:={b,c,d,(b^2+c^2+d^2+b+c+d)/a}; NestList[nxt,{1,1,1,1},12][[All,1]] (* _Harvey P. Dale_, Mar 10 2017 *)
%o A276271 (Ruby)
%o A276271 def A(m, n)
%o A276271   a = Array.new(m, 1)
%o A276271   ary = [1]
%o A276271   while ary.size < n + 1
%o A276271     i = a[1..-1].inject(0){|s, i| s + i * i} + a[1..-1].inject(:+)
%o A276271     break if i % a[0] > 0
%o A276271     a = *a[1..-1], i / a[0]
%o A276271     ary << a[0]
%o A276271   end
%o A276271   ary
%o A276271 end
%o A276271 def A276271(n)
%o A276271   A(4, n)
%o A276271 end
%Y A276271 Cf. A101879, A276122.
%K A276271 nonn
%O A276271 0,5
%A A276271 _Seiichi Manyama_, Aug 26 2016