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A254132
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a(0)=1 and a(1)=2, then each term is x + y + x*y where x and y are the 2 last terms.
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2
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1, 2, 5, 17, 107, 1943, 209951, 408146687, 85691213438975, 34974584955819144511487, 2997014624388697307377363936018956287, 104819342594514896999066634490728502944926883876041385836543
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history;
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OFFSET
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0,2
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LINKS
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Ana Rechtman, Solution, (in French), Images des Mathématiques, CNRS, 2015.
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FORMULA
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a(n) = a(n-1) + a(n-2) + a(n-1)*a(n-2).
a(0) = 1 and a(n) = 2^Fibonacci(n)*3^Fibonacci(n+1) - 1 (see 2nd link).
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EXAMPLE
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a(0) = 1, a(1) = 2, a(2) = 1+2+(1*2) = 5, a(3) = 2+5+(2*5) = 17.
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MATHEMATICA
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a254132[0]=1; a254132[n_]:=2^Fibonacci[n-1]*3^Fibonacci[n]-1;
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PROG
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(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; ); }
(PARI) a(n) = if (!n, 1, 2^fibonacci(n)*3^fibonacci(n+1) - 1);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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