OFFSET
0,4
COMMENTS
The polynomial ratio is near 1.2079333633029512. I got about four of these by switching f[n-1] and f[n-2] and f[n-f[n-1]] and f[n-f[n-2]]: this is the one with the lowest dip in the curve.
FORMULA
( using f[n] for f(n)) f[n] = f[f[n - 1]] + If[n < 8, f[n - f[( n - 1)]], If[Mod[n, 8] == 0, f[f[n/8]], If[Mod[1 + n, 8] == 1, f[f[(n - 1)/8]], If[Mod[2 + n, 8] == 2, f[f[(n - 2)/8]], If[Mod[3 + n, 8] == 3, f[f[(n - 3)/8]], If[ Mod[4 + n, 8] == 4, f[f[(n - 4)/8]], If[Mod[5 + n, 8] == 5, f[f[(n - 5)/8]], If[ Mod[6 + n, 8] == 6, f[f[(n - 6)/8]], If[Mod[7 + n, 8] == 7, f[f[(n - 7)/8]], f[n - f[(n - 1)]]]]]]]]]]]
MATHEMATICA
f[0] = 0; f[1] = 1; f[2] = 1; f[n_] := f[n] = f[f[n - 1]] + If[n < 8, f[n - f[(n - 1)]], If[ Mod[n, 8] == 0, f[f[n/8]], If[Mod[1 + n, 8] == 1, f[f[(n - 1)/8]], If[Mod[2 + n, 8] == 2, f[f[(n - 2)/8]], If[Mod[3 + n, 8] == 3, f[f[(n - 3)/8]], If[Mod[4 + n, 8] == 4, f[f[(n - 4)/8]], If[ Mod[5 + n, 8] == 5, f[f[(n - 5)/8]], If[Mod[6 + n, 8] == 6, f[f[(n - 6)/8]], If[ Mod[7 + n, 8] == 7, f[f[(n - 7)/8]], f[n - f[(n - 1)]]]]]]]]]]] Table[f[n], {n, 0, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Nov 17 2008
STATUS
approved