|
%I #38 Nov 20 2016 03:27:40
%S 1,1,1,1,1,2,4,12,108,10584,27454896,94148851006224,
%T 246222177535609206635748240,
%U 62371770277951054762478578990896212287188931341600,3750595553941161278345366267513070968239986992860645038477600300348697171928615364721752014400
%N a(n) = a(n-1) * a(n-4) * (a(n-2) * a(n-3) + 1) / a(n-5), with a(0) = a(1) = a(2) = a(3) = a(4) = 1.
%C Inspired by Somos-5 sequence.
%C a(n) is integer for n >= 0.
%C a(n+1)/a(n) is integer for n >= 0.
%H Seiichi Manyama, <a href="/A276534/b276534.txt">Table of n, a(n) for n = 0..17</a>
%F a(n) * a(n-5) = a(n-1) * a(n-4) + a(n-1) * a(n-2) * a(n-3) * a(n-4).
%F a(4-n) = a(n).
%F Let b(n) = b(n-4) * (b(n-2) * (b(0) * b(1) * ... * b(n-3))^2 + 1) with b(0) = b(1) = b(2) = b(3) = 1, then a(n) = a(n-1) * b(n-1) = b(0) * b(1) * ... * b(n-1) for n > 0.
%e a(5) = a(4) * b(4) = 1 * 2 = 2,
%e a(6) = a(5) * b(5) = 2 * 2 = 4,
%e a(7) = a(6) * b(6) = 4 * 3 = 12,
%e a(8) = a(7) * b(7) = 12 * 9 = 108.
%o (Ruby)
%o def A(k, n)
%o a = Array.new(2 * k + 1, 1)
%o ary = [1]
%o while ary.size < n + 1
%o i = 0
%o k.downto(1){|j|
%o i += 1
%o i *= a[j] * a[-j]
%o }
%o break if i % a[0] > 0
%o a = *a[1..-1], i / a[0]
%o ary << a[0]
%o end
%o ary
%o end
%o def A276534(n)
%o A(2, n)
%o end
%Y Cf. A006721, A276535.
%K nonn
%O 0,6
%A _Seiichi Manyama_, Nov 16 2016
| 