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

%I A142471 #33 Jan 09 2025 09:52:10
%S A142471 0,0,2,2,6,14,86,1206,103718,125083910,12973452977382,
%T A142471 1622770224612082123622,21052933202100473722674133293917606,
%U A142471 34164073141115747076263787631563122725393126176374288934
%N A142471 a(0) = a(1) = 0; thereafter a(n) = a(n-1)*a(n-2) + 2.
%H A142471 Vincenzo Librandi, <a href="/A142471/b142471.txt">Table of n, a(n) for n = 0..19</a>
%H A142471 A. V. Aho and N. J. A. Sloane, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/11-4/aho-a.pdf">Some doubly exponential sequences</a>, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437.
%H A142471 A. V. Aho and N. J. A. Sloane, <a href="/A000058/a000058.pdf">Some doubly exponential sequences</a>, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)
%F A142471 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
%p A142471 a:= proc(n) option remember;
%p A142471       if n<2 then 0
%p A142471     else a(n-1)*a(n-2) + 2
%p A142471       fi; end:
%p A142471 seq(a(n), n=0..15); # _G. C. Greubel_, Apr 03 2021
%t A142471 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 *)
%o A142471 (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
%o A142471 (Sage)
%o A142471 def a(n): return 0 if n<2 else a(n-1)*a(n-2) + 2
%o A142471 [a(n) for n in (0..15)] # _G. C. Greubel_, Apr 03 2021
%Y A142471 Cf. A000058, A007660, A143684.
%K A142471 nonn
%O A142471 0,3
%A A142471 _N. J. A. Sloane_, based on email from Carla J. Garner-Bennett, Nov 13 2008