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A256663
Nonnegative part of the minimal alternating Fibonacci representation of n.
5
0, 1, 2, 3, 5, 5, 8, 8, 8, 14, 13, 13, 13, 13, 22, 23, 21, 22, 21, 21, 21, 21, 35, 36, 37, 39, 34, 35, 36, 34, 35, 34, 34, 34, 34, 56, 57, 58, 60, 60, 63, 63, 55, 56, 57, 58, 60, 55, 56, 57, 55, 56, 55, 55, 55, 55, 90, 91, 92, 94, 94, 97, 97, 97, 103, 102
OFFSET
0,3
COMMENTS
See A256655 for definitions.
LINKS
FORMULA
A256663(n) - A256664(n) = n.
EXAMPLE
R(9) = 13 - 5 + 1, so that a(9) = 13 + 1 = 14.
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[23];
r[0] = {0}; r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
Table[Total[Abs[r[n]]], {n, 0, 100}] (* A256662 *)
Table[Total[(Abs[r[n]] + r[n])/2], {n, 0, 100}] (* A256663 *)
Table[Total[(Abs[r[n]] - r[n])/2], {n, 0, 100}] (* A256664 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 08 2015
STATUS
approved