I would be grateful if someone could help me with this problem. I define two series recursively, thus:
Subscript[f, 0][n_] := Subscript[f, 0][n - 1] + Subscript[f, 1][n - 2]
Subscript[f, 1][n_] := Subscript[f, 0][n - 1] + Subscript[f, 1][n - 1]
Subscript[f, 0][1] = 0
Subscript[f, 0][2] = 1
Subscript[f, 1][1] = 1
Subscript[f, 1][2] = 1
Mathematica lists the first few values (from index 1 on) just fine, but for some reason it can't find out the values of the two series for indices below 1. And RSolve
can't figure out the closed formula for any of the series.
But this should be easy, say if $f_0(2)=f_0(1)+f_1(0)$, then $f_1(0)=f_0(2)-f_0(1)=1$. I thought Mathematica could extrapolate series like that.
f1[-2]
$\endgroup$ – Dr. belisarius Feb 26 '15 at 20:40