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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 (list; graph; refs; listen; history; text; internal format)
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+2sqrt(2)+(1-2sqrt(2))(-1)^n)/2. - Paul Barry, Apr 26 2004

The sequence 2,1,4,2,8,... has a(n)=2^(n/2)(1+2sqrt(2)-(1-2sqrt(2))(-1)^n)/(2sqrt(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).

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). - Colin Barker, Oct 14 2014

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 A106489

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

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Last modified May 13 08:08 EDT 2021. Contains 343836 sequences. (Running on oeis4.)