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A276258 a(n) = 4*a(n-1)*a(n-2) - a(n-3), with a(1) = a(2) = a(3) = 1.

%I A276258 #26 Sep 04 2016 23:26:46
%S A276258 1,1,1,3,11,131,5761,3018753,69564144001,839987873581797251,
%T A276258 233732149587751710483796746251,
%U A276258 785328685279672432967483833110876164468741280003,734226246973363127354668827312570246092792043625372932024478449584047744277761
%N A276258 a(n) = 4*a(n-1)*a(n-2) - a(n-3), with a(1) = a(2) = a(3) = 1.
%H A276258 Seiichi Manyama, <a href="/A276258/b276258.txt">Table of n, a(n) for n = 1..18</a>
%F A276258 a(1)=a(2)=a(3)=1; a(n)=(a(n-1)^2+a(n-2)^2+1)/a(n-3).
%F A276258 a(n) ~ 1/4 * c^(((1+sqrt(5))/2)^n), where c = 1.41452525081158447693692520473959... . - _Vaclav Kotesovec_, Aug 26 2016
%F A276258 a(n)*a(n+1)*a(n+2) = (a(n)^2+a(n+1)^2+a(n+2)^2+1)/4. - _Seiichi Manyama_, Sep 04 2016
%t A276258 RecurrenceTable[{a[n] == 4*a[n - 1]*a[n - 2] - a[n - 3], a[1] == 1,
%t A276258   a[2] == 1, a[3] == 1}, a, {n, 1, 10}] (* _G. C. Greubel_, Aug 25 2016 *)
%o A276258 (Ruby)
%o A276258 def A(m, n)
%o A276258   a = Array.new(m, 1)
%o A276258   ary = [1]
%o A276258   while ary.size < n
%o A276258     a = *a[1..-1], *a[1..-1].inject(:*) * (m + 1) - a[0]
%o A276258     ary << a[0]
%o A276258   end
%o A276258   ary
%o A276258 end
%o A276258 def A276258(n)
%o A276258   A(3, n)
%o A276258 end
%Y A276258 Cf. A001519, A064098, A276256, A276259.
%K A276258 nonn
%O A276258 1,4
%A A276258 _Seiichi Manyama_, Aug 25 2016