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A254132 a(0)=1 and a(1)=2, then each term is x + y + x*y where x and y are the 2 last terms.

%I A254132 #21 Oct 19 2024 15:57:32
%S A254132 1,2,5,17,107,1943,209951,408146687,85691213438975,
%T A254132 34974584955819144511487,2997014624388697307377363936018956287,
%U A254132 104819342594514896999066634490728502944926883876041385836543
%N A254132 a(0)=1 and a(1)=2, then each term is x + y + x*y where x and y are the 2 last terms.
%H A254132 Ana Rechtman, <a href="http://images-archive.math.cnrs.fr/Janvier-2015-3eme-defi.html">Janvier 2015, 3ème défi</a>, (in French), Images des Mathématiques, CNRS, 2015.
%H A254132 Ana Rechtman, <a href="http://images-archive.math.cnrs.fr/Janvier-2015-4eme-defi.html">Solution</a>, (in French), Images des Mathématiques, CNRS, 2015.
%F A254132 a(n) = a(n-1) + a(n-2) + a(n-1)*a(n-2).
%F A254132 a(0) = 1 and a(n) = 2^Fibonacci(n)*3^Fibonacci(n+1) - 1 (see 2nd link).
%F A254132 a(n) == 8 mod 9, for n > 2. - _Ivan N. Ianakiev_, Jan 27 2015
%e A254132 a(0) = 1, a(1) = 2, a(2) = 1+2+(1*2) = 5, a(3) = 2+5+(2*5) = 17.
%t A254132 a254132[0]=1;a254132[n_]:=2^Fibonacci[n-1]*3^Fibonacci[n]-1;
%t A254132 a254132/@Range[0,11] (* _Ivan N. Ianakiev_, Jan 27 2015 *)
%o A254132 (PARI) lista(nn) = {x = 1; y = 2; print1(x, ", ", y, ", "); for (j=1, nn, z = x + y + x*y; print1(z, ", "); x = y; y = z;);}
%o A254132 (PARI) a(n) = if (!n, 1, 2^fibonacci(n)*3^fibonacci(n+1) - 1);
%Y A254132 Cf. A000045 (Fibonacci), A063896 (similar, with initial values 0,1).
%Y A254132 Cf. A198796 (2^n*3^(n+1)-1).
%K A254132 nonn
%O A254132 0,2
%A A254132 _Michel Marcus_, Jan 26 2015