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a(n) = a(n-1) + 2^a(n-2).
2

%I #21 Jan 05 2024 19:14:02

%S 0,0,1,2,4,8,24,280,16777496,

%T 1942668892225729070919461906823518906642406839052139521251812409738904285205225275672

%N a(n) = a(n-1) + 2^a(n-2).

%C The next term is too large to include.

%C The next term has 5050530 digits. - _Harvey P. Dale_, Jan 05 2024

%D D. E. Knuth, personal communication.

%t Off[General::ovfl];a={1,0};Flatten[Prepend[Table[s=Plus@@a;a=2^(RotateLeft[a]);a[[ -1]]=s,{n,8}],Table[0,{m,Length[a]-1}]]] (* _Vladimir Joseph Stephan Orlovsky_, Nov 18 2009 *)

%t nxt[{a_,b_}]:={b,b+2^a}; NestList[nxt,{0,0},9][[;;,1]] (* _Harvey P. Dale_, Jan 05 2024 *)

%Y Cf. A000659.

%K nonn

%O 0,4

%A _N. J. A. Sloane_

%E 1 more term from _Vladeta Jovovic_, Mar 19 2000