A276122 a(0) = a(1) = a(2) = 1; for n > 2, a(n) = (a(n-1)^2+a(n-2)^2+a(n-1)+a(n-2))/a(n-3).

1, 1, 1, 4, 22, 526, 69427, 219111589, 91273561736491, 119994570874632853695766, 65713991236617279734602790963627271046, 47311933073383646516067037755547920981262829886906923065810924

Offset: 0

Author

Bruno Langlois, Aug 21 2016

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..16

Crossrefs

Cf. A064098, A072881, A101879, A165903.

Programs

Mathematica

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

Formula

a(n) = 6*a(n-1)*a(n-2)-a(n-3)-1.

a(n) ~ 1/6 * c^(phi^n), where c = 2.059783590102273... and phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Mar 20 2017

Extensions

a(10) corrected by Seiichi Manyama, Aug 21 2016