A276124 a(0) = a(1) = a(2) = a(3) = 1; for n > 3, a(n) = (a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-1)*a(n-2)*a(n-3))/a(n-4).

1, 1, 1, 1, 4, 22, 589, 399253, 41144206447, 77387327118194895379, 10169897514576967837097322386922878932, 259050897146323086186965020577200627526185475088368701480903471601830

Offset: 0

Author

Bruno Langlois, Aug 21 2016

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..15

Crossrefs

Cf. A165903, A072878.

Programs

Mathematica

RecurrenceTable[{a[n] == (a[n - 1]^2 + a[n - 2]^2 + a[n - 3]^2 + a[n - 1] a[n - 2] a[n - 3])/a[n - 4], a[0] == a[1] == a[2] == a[3] == 1}, a, {n, 0, 11}] (* Michael De Vlieger, Aug 21 2016 *)

Ruby

def A(m, n)
  a = Array.new(m, 1)
  ary = [1]
  while ary.size < n + 1
    i = a[1..-1].inject(0){|s, i| s + i * i} + a[1..-1].inject(:*)
    break if i % a[0] > 0
    a = *a[1..-1], i / a[0]
    ary << a[0]
  end
  ary
end
def A276124(n)
  A(4, n)
end # Seiichi Manyama, Aug 21 2016

Formula

a(n) = 8*a(n-1)*a(n-2)*a(n-3)-a(n-1)*a(n-2)-a(n-1)*a(n-3)-a(n-2)*a(n-3)-a(n-4).