A276535 a(n) = a(n-1) * a(n-6) * (a(n-2) * a(n-5) * (a(n-3) * a(n-4) + 1) + 1) / a(n-7), with a(0) = a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = 1.

1, 1, 1, 1, 1, 1, 1, 3, 9, 63, 2331, 4114215, 16341764835375, 266584861903285121344257375, 7896333852271846954822982651737848156847060737115875, 2309336603704915706429640788623787983392652603516450553629239932054220008270731649775618317371336467375

Offset: 0

Author

Seiichi Manyama, Nov 16 2016

Keywords

• nonn

Comments

Inspired by Somos-7 sequence.

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

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

Examples

			a(7) = a(6) * b(6) = 1 * 3 = 3,
a(8) = a(7) * b(7) = 3 * 3 = 9,
a(9) = a(8) * b(8) = 9 * 7 = 63,
a(10) = a(9) * b(9) = 63 * 37 = 2331.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..18

Crossrefs

Cf. A006723, A276534.

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 A276535(n)
  A(3, n)
end

Formula

a(n) * a(n-7) = a(n-1) * a(n-6) + a(n-1) * a(n-2) * a(n-5) * a(n-6) + a(n-1) * a(n-2) * a(n-3) * a(n-4) * a(n-5) * a(n-6).

a(6-n) = a(n).

Let b(n) = b(n-6) * (b(n-2) * b(n-3) * b(n-4) * (b(0) * b(1) * ... * b(n-5))^2 * (b(n-3) * (b(0) * b(1) * ... * b(n-4))^2 + 1)+ 1) with b(0) = b(1) = b(2) = b(3) = b(4) = b(5) = 1, then a(n) = a(n-1) * b(n-1) = b(0) * b(1) * ... * b(n-1) for n > 0.