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.

1, 2, 5, 17, 107, 1943, 209951, 408146687, 85691213438975, 34974584955819144511487, 2997014624388697307377363936018956287, 104819342594514896999066634490728502944926883876041385836543

Offset

0,2

Links

Table of n, a(n) for n=0..11.

Ana Rechtman, Janvier 2015, 3ème défi, (in French), Images des Mathématiques, CNRS, 2015.

Ana Rechtman, Solution, (in French), Images des Mathématiques, CNRS, 2015.

Formula

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).

a(n) == 8 mod 9, for n > 2. - Ivan N. Ianakiev, Jan 27 2015

Example

a(0) = 1, a(1) = 2, a(2) = 1+2+(1*2) = 5, a(3) = 2+5+(2*5) = 17.

Mathematica

a254132[0]=1; a254132[n_]:=2^Fibonacci[n-1]*3^Fibonacci[n]-1;
a254132/@Range[0, 11] (* Ivan N. Ianakiev, Jan 27 2015 *)

Prog

(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);

Crossrefs

Cf. A000045 (Fibonacci), A063896 (similar, with initial values 0,1).

Cf. A198796 (2^n*3^(n+1)-1).

Sequence in context: A143878 A081546 A103511 * A161609 A228238 A174168

Adjacent sequences: A254129 A254130 A254131 * A254133 A254134 A254135

Keyword

nonn

Author

Michel Marcus, Jan 26 2015

Status

approved