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A276266 a(0) = a(1) = a(2) = 1; for n>2, a(n) = ( a(n-1)*a(n-2) + 1 )^2 / a(n-3).

%I A276266 #17 Aug 27 2016 02:23:58
%S A276266 1,1,1,4,25,10201,16259565169,1100432328310492581042546436,
%T A276266 31383529740086705883339675381564403354342372463018335778292540655564225
%N A276266 a(0) = a(1) = a(2) = 1; for n>2, a(n) = ( a(n-1)*a(n-2) + 1 )^2 / a(n-3).
%H A276266 Seiichi Manyama, <a href="/A276266/b276266.txt">Table of n, a(n) for n = 0..10</a>
%F A276266 a(n) = A208209(n)^2.
%t A276266 RecurrenceTable[{a[n] == (a[n - 1] a[n - 2] + 1)^2/a[n - 3], a[0] == a[1] == a[2] == 1}, a, {n, 0, 8}] (* _Michael De Vlieger_, Aug 26 2016 *)
%o A276266 (Ruby)
%o A276266 def A(m, n)
%o A276266   a = Array.new(m, 1)
%o A276266   ary = [1]
%o A276266   while ary.size < n + 1
%o A276266     i = a[1..-1].inject(:*) + 1
%o A276266     i *= i
%o A276266     break if i % a[0] > 0
%o A276266     a = *a[1..-1], i / a[0]
%o A276266     ary << a[0]
%o A276266   end
%o A276266   ary
%o A276266 end
%o A276266 def A276266(n)
%o A276266   A(3, n)
%o A276266 end
%Y A276266 Cf. A081068, A208209.
%K A276266 nonn
%O A276266 0,4
%A A276266 _Seiichi Manyama_, Aug 26 2016