A258948 a(1)=1, a(2)=2; for n>2, a(n) = (1/2)*a(n-1)*a(n-2) + a(n-1) + a(n-2).

1, 2, 4, 10, 34, 214, 3886, 419902, 816293374, 171382426877950, 69949169911638289022974, 5994029248777394614754727872037912574, 209638685189029793998133268981457005889853767752082771673086

Offset: 1

Author

Morris Neene, Jun 15 2015

Keywords

• nonn
• easy

Comments

a(n) + 2 = (1/2)*(a(n-1) + 2)*(a(n-2) + 2), from which the general formula can be proved using the method shown in A063896.

Examples

			a(3) = (1/2)*2*1 + 2 + 1 = 4;
a(4) = (1/2)*4*2 + 4 + 2 = 10;
a(5) = (1/2)*10*4 + 10 + 4 = 34;
a(6) = 2*(3^3)(2^2) - 2 = 214.
		

Crossrefs

Cf. A000045, A063896, A100701, A254132.

Programs

Magma

[n le 2 select n else Self(n-1)*Self(n-2)/2+Self(n-1)+Self(n-2): n in [1..13]];

Magma

[2*3^Fibonacci(n-2)*2^Fibonacci(n-3)-2: n in [1..20]]; // Vincenzo Librandi, Jun 17 2015

Mathematica

Table[2 3^Fibonacci[n-2] 2^Fibonacci[n-3] - 2, {n, 1, 20}] (* Vincenzo Librandi, Jun 17 2015 *)

PARI

a(n) = 2*(3^fibonacci(n-2))*(2^fibonacci(n-3)) - 2; \\ Michel Marcus, Jun 17 2015

Formula

a(n) = 2 * 3^A000045(n-2) * 2^A000045(n-3) - 2, where A000045(n) is the n-th Fibonacci number.