A276258 a(n) = 4*a(n-1)*a(n-2) - a(n-3), with a(1) = a(2) = a(3) = 1.

1, 1, 1, 3, 11, 131, 5761, 3018753, 69564144001, 839987873581797251, 233732149587751710483796746251, 785328685279672432967483833110876164468741280003, 734226246973363127354668827312570246092792043625372932024478449584047744277761

Offset: 1

Author

Seiichi Manyama, Aug 25 2016

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..18

Crossrefs

Cf. A001519, A064098, A276256, A276259.

Programs

Mathematica

RecurrenceTable[{a[n] == 4*a[n - 1]*a[n - 2] - a[n - 3], a[1] == 1,
  a[2] == 1, a[3] == 1}, a, {n, 1, 10}] (* G. C. Greubel, Aug 25 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 A276258(n)
  A(3, n)
end

Formula

a(1)=a(2)=a(3)=1; a(n)=(a(n-1)^2+a(n-2)^2+1)/a(n-3).

a(n) ~ 1/4 * c^(((1+sqrt(5))/2)^n), where c = 1.41452525081158447693692520473959... . - Vaclav Kotesovec, Aug 26 2016

a(n)*a(n+1)*a(n+2) = (a(n)^2+a(n+1)^2+a(n+2)^2+1)/4. - Seiichi Manyama, Sep 04 2016