OFFSET
0,4
COMMENTS
Comments from Jon Maiga, Aug 25 2019: (Start)
The function seems to follow the square root of n.
The first differences center around the x-axis with a similar look.
Changing the initial values to for example f(0)=1 and f(1)=3 creates a very different graph.
See the image for fractional versions with f(0)=f(1)=1 and f(0)=1, f(1)=3.
(End)
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
J. Maiga, A few good looking recursive functions, 2019.
Jon Maiga, Plots of f(n) for n up to 1000
MAPLE
L[0]:= 1: R[0]:= 1: A[0]:= 1:
L[1]:= 1: R[1]:= 1: A[1]:= 1:
for n from 2 to 100 do
x:= (n - R[n-1])/R[n-2];
y:= (n - L[n-1])/L[n-2];
L[n]:= 10^(-100)*floor(x*10^100);
R[n]:= 10^(-100)*ceil(y*10^100);
if round(L[n]) <> round(R[n]) then printf("Oops: %d \n", n); break fi;
A[n]:= round(L[n])
od:
seq(A[n], n=0..100); # Robert Israel, Aug 24 2019
MATHEMATICA
f[0] = f[1] = 1;
f[n_] := f[n] = N[(n - f[n - 1])/f[n - 2]]
Round[Array[f, 83, 0]]
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Jon Maiga, Jun 11 2019
STATUS
approved