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