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

1,4

Comments

The sequence 1,4,2,8,4,... has g.f. (1+4x)/(1-2x^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).

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)

Mathematica

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

Crossrefs

Cf. A005246, A076737.

Sequence in context: A265256 A135530 A137206 * A182906 A193359 A344613

Adjacent sequences: A076733 A076734 A076735 * A076737 A076738 A076739

Keyword

frac,nonn,easy

Author

Benoit Cloitre, Nov 24 2002

Extensions

More terms from Paul Barry, Apr 26 2004

Status

approved