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 A276534 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. 2

%I

%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

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Last modified October 20 04:37 EDT 2019. Contains 328247 sequences. (Running on oeis4.)