A276532 a(n) = (a(n-1) * a(n-6) + a(n-2) * a(n-3) * a(n-4) * a(n-5)) / 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, 2, 3, 5, 11, 41, 371, 7507, 429563, 419408854, 9811194604889, 45615501062085527113, 323645006689468299915979814409, 217332607887523478570092794860281557159140687, 8092345737591989154121803868154457767563221634145658745306515944569

Offset: 0

Author

Seiichi Manyama, Nov 16 2016

Keywords

• nonn

Comments

This sequence is one generalization of Dana Scott's sequence (A048736).

a(n) is an integer for all n.

The recursion exhibits the Laurent phenomenon. See A278706 for the exponents of the denominator of the Laurent polynomial. - Michael Somos, Nov 26 2016

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..26

Crossrefs

Cf. A048736, A006721, A276531, A278706.

Programs

Ruby

def A(k, n)
  a = Array.new(k, 1)
  ary = [1]
  while ary.size < n + 1
    i = a[-1] * a[1] + a[2..-2].inject(:*)
    break if i % a[0] > 0
    a = *a[1..-1], i / a[0]
    ary << a[0]
  end
  ary
end
def A276532(n)
  A(7, n)
end

Formula

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

a(6-n) = a(n) for all n in Z.