A276259 a(n) = 5*a(n-1)*a(n-2)*a(n-3) - a(n-4) with n>4, a(1) = a(2) = a(3) = a(4) = 1.

1, 1, 1, 1, 4, 19, 379, 144019, 5185404091, 1415179768826376436, 5284257989697826589787882104688841, 193886796198316302609610159795591363955441027433554915785933561

Offset: 1

Author

Seiichi Manyama, Aug 26 2016

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..16

Crossrefs

Cf. A001519, A276258.

Programs

Mathematica

RecurrenceTable[{a[n] == 5 a[n - 1] a[n - 2] a[n - 3] - a[n - 4], a[1] == a[2] == a[3] == a[4] == 1}, a, {n, 12}] (* Michael De Vlieger, Aug 26 2016 *)

Ruby

def A(m, n)
  a = Array.new(m, 1)
  ary = [1]
  while ary.size < n
    a = *a[1..-1], *a[1..-1].inject(:*) * (m + 1) - a[0]
    ary << a[0]
  end
  ary
end
def A276259(n)
  A(4, n)
end

Formula

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

a(n)*a(n+1)*a(n+2)*a(n+3) = (a(n)^2 + a(n+1)^2 + a(n+2)^2 + a(n+3)^2 + 1)/5.