OFFSET
1,1
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
EXAMPLE
Let R(k) be the minimal alternating Fibonacci representation of k. The trace of R(k) is the last term.
R(1) = 1, trace = 1
R(2) = 2, trace = 2
R(3) = 3, trace = 3
R(4) = 5 - 1, trace = -1
R(5) = 5, trace = 5
R(6) = 6 - 2, trace = -2
MATHEMATICA
b[n_] = Fibonacci[n]; bb = Table[b[n], {n, 1, 70}];
h[0] = {1}; h[n_] := Join[h[n - 1], Table[b[n + 2], {k, 1, b[n]}]];
g = h[18]; r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]]
t = Table[Last[r[n]], {n, 0, 1000}]; (* A256656 *)
Select[Range[200], Last[r[#]] > 0 &] (* A256656 *)
Select[Range[200], Last[r[#]] < 0 &] (* A256657 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 08 2015
STATUS
approved