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A276259 a(n) = 5*a(n-1)*a(n-2)*a(n-3) - a(n-4) with n>4, a(1) = a(2) = a(3) = a(4) = 1.

%I A276259 #21 Sep 07 2016 08:13:40
%S A276259 1,1,1,1,4,19,379,144019,5185404091,1415179768826376436,
%T A276259 5284257989697826589787882104688841,
%U A276259 193886796198316302609610159795591363955441027433554915785933561
%N A276259 a(n) = 5*a(n-1)*a(n-2)*a(n-3) - a(n-4) with n>4, a(1) = a(2) = a(3) = a(4) = 1.
%H A276259 Seiichi Manyama, <a href="/A276259/b276259.txt">Table of n, a(n) for n = 1..16</a>
%F A276259 a(1)=a(2)=a(3)=a(4)=1; for n>4, a(n) = (a(n-1)^2 + a(n-2)^2 + a(n-3)^2 + 1) / a(n-4).
%F A276259 a(n)*a(n+1)*a(n+2)*a(n+3) = (a(n)^2 + a(n+1)^2 + a(n+2)^2 + a(n+3)^2 + 1)/5.
%t A276259 RecurrenceTable[{a[n] == 5 a[n - 1] a[n - 2] a[n - 3] - a[n - 4], a[1] == a[2] == a[3] == a[4] == 1}, a, {n, 12}] (* _Michael De Vlieger_, Aug 26 2016 *)
%o A276259 (Ruby)
%o A276259 def A(m, n)
%o A276259   a = Array.new(m, 1)
%o A276259   ary = [1]
%o A276259   while ary.size < n
%o A276259     a = *a[1..-1], *a[1..-1].inject(:*) * (m + 1) - a[0]
%o A276259     ary << a[0]
%o A276259   end
%o A276259   ary
%o A276259 end
%o A276259 def A276259(n)
%o A276259   A(4, n)
%o A276259 end
%Y A276259 Cf. A001519, A276258.
%K A276259 nonn
%O A276259 1,5
%A A276259 _Seiichi Manyama_, Aug 26 2016