login
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).
5
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
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
Sequence in context: A265256 A135530 A137206 * A182906 A193359 A344613
KEYWORD
frac,nonn,easy
AUTHOR
Benoit Cloitre, Nov 24 2002
EXTENSIONS
More terms from Paul Barry, Apr 26 2004
STATUS
approved