A256663 Nonnegative part of the minimal alternating Fibonacci representation of n.

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

Clark Kimberling, Table of n, a(n) for n = 0..1000

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

Cf. A000045, A256655, A256662, A256664.

Sequence in context: A246104 A256654 A204926 * A188201 A184165 A152771

Adjacent sequences: A256660 A256661 A256662 * A256664 A256665 A256666

Keyword

nonn,easy

Author

Clark Kimberling, Apr 08 2015

Status

approved