A142471 a(0) = a(1) = 0; thereafter a(n) = a(n-1)*a(n-2) + 2.

0, 0, 2, 2, 6, 14, 86, 1206, 103718, 125083910, 12973452977382, 1622770224612082123622, 21052933202100473722674133293917606, 34164073141115747076263787631563122725393126176374288934

Offset: 0

Author

N. J. A. Sloane, based on email from Carla J. Garner-Bennett, Nov 13 2008

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..19
• A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437.
• A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)

Crossrefs

Cf. A000058, A007660, A143684.

Programs

Magma

I:=[0,0]; [n le 2 select I[n] else Self(n-1)*Self(n-2)+2: n in [1..15]]; // Vincenzo Librandi, Nov 14 2011

Maple

a:= proc(n) option remember;
      if n<2 then 0
    else a(n-1)*a(n-2) + 2
      fi; end:
seq(a(n), n=0..15); # G. C. Greubel, Apr 03 2021

Mathematica

a[0] = a[1] = 0; a[n_] := a[n-1] a[n-2] + 2; Table[a[n], {n, 0, 15}] (* T. D. Noe, Nov 14 2011 *)

Sage

def a(n): return 0 if n<2 else a(n-1)*a(n-2) + 2
[a(n) for n in (0..15)] # G. C. Greubel, Apr 03 2021

Formula

a(n) ~ c^(phi^n), where c = 1.278178162398588325773605473403497130099080978627235683548955136178125... and phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, May 21 2015