A256664 Nonpositive part of the minimal alternating Fibonacci representation of n.

0, 0, 0, 0, 1, 0, 2, 1, 0, 5, 3, 2, 1, 0, 8, 8, 5, 5, 3, 2, 1, 0, 13, 13, 13, 14, 8, 8, 8, 5, 5, 3, 2, 1, 0, 21, 21, 21, 22, 21, 23, 22, 13, 13, 13, 13, 14, 8, 8, 8, 5, 5, 3, 2, 1, 0, 34, 34, 34, 35, 34, 36, 35, 34, 39, 37, 36, 35, 21, 21, 21, 21, 22, 21, 23

Offset

0,7

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) = 5.

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, A256663.

Sequence in context: A324162 A060136 A327358 * A226783 A245972 A088391

Adjacent sequences: A256661 A256662 A256663 * A256665 A256666 A256667

Keyword

nonn,easy

Author

Clark Kimberling, Apr 08 2015

Status

approved