A276268 a(0) = a(1) = a(2) = a(3) = 1; for n>3, a(n) = ( a(n-1)*a(n-2)*a(n-3) + 1 )^2 / a(n-4).

1, 1, 1, 1, 4, 25, 10201, 1040606050201, 17606710134796383100801078407630169, 1397251576763829044923817239566095383950667477080314561212188721224520791793149263311589905001958916

Offset: 0

Author

Seiichi Manyama, Aug 26 2016

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..11

Crossrefs

Cf. A081068, A276266, A276267.

Programs

Mathematica

RecurrenceTable[{a[n] == (a[n - 1] a[n - 2] a[n - 3] + 1)^2/a[n - 4], a[0] == a[1] == a[2] == a[3] == 1}, a, {n, 0, 10}] (* Michael De Vlieger, Aug 26 2016 *)
nxt[{a_,b_,c_,d_}]:={b,c,d,(b*c*d+1)^2/a}; NestList[nxt,{1,1,1,1},10][[All,1]] (* Harvey P. Dale, Jan 31 2020 *)

Ruby

def A(m, n)
  a = Array.new(m, 1)
  ary = [1]
  while ary.size < n + 1
    i = a[1..-1].inject(:*) + 1
    i *= i
    break if i % a[0] > 0
    a = *a[1..-1], i / a[0]
    ary << a[0]
  end
  ary
end
def A276268(n)
  A(4, n)
end

Formula

a(n) = A276267(n)^2.