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A sequence of words over an alphabet of two letters: a(0) = 1, a(1) = 2; a(n+2) = a(n+1)a(n)a(n+1).
1

%I #9 Jun 05 2021 10:22:52

%S 1,2,212,2122212,21222122122122212,

%T 21222122122122212212221221222122122122212,

%U 212221221221222122122212212221221221222122122212212212221221222122122122212212221221222122122122212

%N A sequence of words over an alphabet of two letters: a(0) = 1, a(1) = 2; a(n+2) = a(n+1)a(n)a(n+1).

%C A055642(a(n)) = A001333(n). - _Reinhard Zumkeller_, Feb 02 2007

%D Suggested by a posting by Igor G. Korepanov to "Jim's Forum", Jan 10 2007.

%F a(n)=(a(n-1)*A011557(A001333(n-2))+a(n-2))*A011557(A001333(n-2))+a(n-1). - _Reinhard Zumkeller_, Feb 02 2007

%t nxt[{a_,b_}]:={b,FromDigits[Flatten[Join[IntegerDigits[b],IntegerDigits[a],IntegerDigits[ b]]]]}; NestList[nxt,{1,2},7][[All,1]] (* _Harvey P. Dale_, Jun 05 2021 *)

%K nonn,base

%O 0,2

%A _N. J. A. Sloane_, Jan 10 2007