A076736 Let u(1) = u(2) = u(3) = 2, u(n) = (1 + u(n-1)*u(n-2))/u(n-3); then a(n) is the denominator of u(n).

1, 1, 1, 2, 1, 4, 2, 8, 4, 16, 8, 32, 16, 64, 32, 128, 64, 256, 128, 512, 256, 1024, 512, 2048, 1024, 4096, 2048, 8192, 4096, 16384, 8192, 32768, 16384, 65536, 32768, 131072, 65536, 262144, 131072, 524288, 262144, 1048576, 524288, 2097152

Offset: 1

Author

Benoit Cloitre, Nov 24 2002

Keywords

• frac
• nonn
• easy

Comments

The sequence 1,4,2,8,4,... has g.f. (1+4*x)/(1-2*x^2) and a(n) = 2^(n/2)*(1+2*sqrt(2) + (1-2*sqrt(2))*(-1)^n)/2. - Paul Barry, Apr 26 2004

The sequence 2,1,4,2,8,... has a(n) = 2^(n/2)*(1+2*sqrt(2)-(1-2*sqrt(2))*(-1)^n)/(2*sqrt(2)) and is essentially the pair-reversal of A016116. - Paul Barry, Apr 26 2004

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,2).

Crossrefs

Cf. A005246, A076737.

Programs

Mathematica

LinearRecurrence[{0,2},{1,1,1,2,1},50] (* Harvey P. Dale, Aug 25 2015 *)

Formula

For n > 4, a(n) = 2^A028242(n-4).

From Colin Barker, Oct 14 2014: (Start)

For n > 5, a(n) = 2*a(n-2).

G.f.: x*(x-1)*(x^3+x^2+2*x+1) / (2*x^2-1). (End)

Extensions

More terms from Paul Barry, Apr 26 2004