A276271 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, 6, 46, 2206, 4870846, 3954191749561, 339905052007042640998641, 52373274877565894156748130733610185904753361, 563138297002425210235477817802336090254190075906443582099838858026136728896536841

Offset: 0

Author

Seiichi Manyama, Aug 26 2016

Keywords

• nonn

Links

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

Crossrefs

Cf. A101879, A276122.

Programs

Mathematica

nxt[{a_,b_,c_,d_}]:={b,c,d,(b^2+c^2+d^2+b+c+d)/a}; NestList[nxt,{1,1,1,1},12][[All,1]] (* Harvey P. Dale, Mar 10 2017 *)

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 A276271(n)
  A(4, n)
end

Formula

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

a(n) ~ 2^(-3/2) * c^(d^n), where c = 1.2578918597... and d = A058265 = 1.83928675521416... = (1 + (19 + 3*sqrt(33))^(1/3) + (19 - 3*sqrt(33))^(1/3))/3. - Vaclav Kotesovec, Mar 20 2017