A256662 Sum of absolute values of terms in the minimal alternating Fibonacci representation of n.

0, 1, 2, 3, 6, 5, 10, 9, 8, 19, 16, 15, 14, 13, 30, 31, 26, 27, 24, 23, 22, 21, 48, 49, 50, 53, 42, 43, 44, 39, 40, 37, 36, 35, 34, 77, 78, 79, 82, 81, 86, 85, 68, 69, 70, 71, 74, 63, 64, 65, 60, 61, 58, 57, 56, 55, 124, 125, 126, 129, 128, 133, 132, 131

Offset

0,3

Comments

The terms are distinct. See A256655 for definitions.

Links

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

Example

Minimal alternating Fibonacci representations:
R(0) = 0
R(1) = 1
R(2) = 2
R(3) = 3
R(4) = 5 - 1, so that a(4) = 6.
R(9) = 13 - 5 + 1, so that a(9) = 19.

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.

Sequence in context: A196330 A332462 A358137 * A055944 A331633 A350801

Adjacent sequences: A256659 A256660 A256661 * A256663 A256664 A256665

Keyword

nonn,easy

Author

Clark Kimberling, Apr 08 2015

Status

approved