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.

1, 1, 1, 1, 1, 2, 4, 12, 108, 10584, 27454896, 94148851006224, 246222177535609206635748240, 62371770277951054762478578990896212287188931341600, 3750595553941161278345366267513070968239986992860645038477600300348697171928615364721752014400

Offset: 0

Author

Seiichi Manyama, Nov 16 2016

Keywords

• nonn

Comments

Inspired by Somos-5 sequence.

a(n) is an integer for n >= 0.

a(n+1)/a(n) is an integer for n >= 0.

Examples

			a(5) = a(4) * b(4) =  1 * 2 =   2,
a(6) = a(5) * b(5) =  2 * 2 =   4,
a(7) = a(6) * b(6) =  4 * 3 =  12,
a(8) = a(7) * b(7) = 12 * 9 = 108.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..17

Crossrefs

Cf. A006721, A276535.

Programs

Ruby

def A(k, n)
  a = Array.new(2 * k + 1, 1)
  ary = [1]
  while ary.size < n + 1
    i = 0
    k.downto(1){|j|
      i += 1
      i *= a[j] * a[-j]
    }
    break if i % a[0] > 0
    a = *a[1..-1], i / a[0]
    ary << a[0]
  end
  ary
end
def A276534(n)
  A(2, n)
end

Formula

a(n) * a(n-5) = a(n-1) * a(n-4) + a(n-1) * a(n-2) * a(n-3) * a(n-4).

a(4-n) = a(n).

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.