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

%I #16 Apr 09 2022 11:36:51

%S 0,0,1,2,5,34,17179869189

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

%C The next term has 5171655948 digits. - _Franklin T. Adams-Watters_, Jul 03 2009

%t Join[{a=0,b=0},Table[c=2^b+a;a=b;b=c,{n,5}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 13 2011 *)

%t nxt[{a_,b_}]:={b,2^b+a}; NestList[nxt,{0,0},6][[All,1]] (* _Harvey P. Dale_, Apr 09 2022 *)

%Y Cf. A000643.

%K nonn

%O 0,4

%A _N. J. A. Sloane_