Rabbit Sequence

Author

Eric W. Weisstein
April 10, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/RabbitSequence.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/RabbitSequence.html.

©2006 Wolfram Research, Inc. except for portions noted otherwise

Recurrence

V7

RSolve[{a[n]==a[n-1](2^(Fibonacci[n-1]))+a[n-2],a[0]==0,a[1]==1},a[n],n]

Enumeration

l=Nest[Flatten[#/.{0->{1},1->{1,0}}]&,{0},10]

a[0]=0;
a[1]=1;
a[n_]:=a[n]=a[n-1]2^Fibonacci[n-1]+a[n-2]

Table[a[n],{n,10}]

Recurrence Plot

l=Nest[Flatten[#/.{0->{1},1->{1,0}}]&,{0},20];

ArrayPlot[Mod[Table[l[[x]]-l[[y]],{x,128},{y,128}],2],PixelConstrained->True]

ArrayPlot[Mod[Table[l[[x]]-l[[y]],{x,128},{y,128}],3],PixelConstrained->True,ColorRules->{0->Yellow,1->Green,2->Blue}]