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

Author

Clark Kimberling, Apr 08 2015

Keywords

• nonn
• easy

Comments

The terms are distinct. See A256655 for definitions.

Examples

			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.
		

Links

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

Crossrefs

Cf. A000045, A256655.

Programs

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 *)