A256662 - OEIS

%I #4 Apr 09 2015 08:02:55

%S 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,

%T 53,42,43,44,39,40,37,36,35,34,77,78,79,82,81,86,85,68,69,70,71,74,63,

%U 64,65,60,61,58,57,56,55,124,125,126,129,128,133,132,131

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

%C The terms are distinct.  See A256655 for definitions.

%H Clark Kimberling, <a href="/A256662/b256662.txt">Table of n, a(n) for n = 0..1000</a>

%e Minimal alternating Fibonacci representations:

%e R(0) = 0

%e R(1) = 1

%e R(2) = 2

%e R(3) = 3

%e R(4) = 5 - 1, so that a(4) = 6.

%e R(9) = 13 - 5 + 1, so that a(9) = 19.

%t b[n_] = Fibonacci[n]; bb = Table[b[n], {n, 1, 70}];

%t h[0] = {1}; h[n_] := Join[h[n - 1], Table[b[n + 2], {k, 1, b[n]}]];

%t g = h[23];  r[0] = {0};

%t r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];

%t Table[Total[Abs[r[n]]], {n, 0, 100}] (* A256662 *)

%t Table[Total[(Abs[r[n]] + r[n])/2], {n, 0, 100}]  (* A256663 *)

%t Table[Total[(Abs[r[n]] - r[n])/2], {n, 0, 100}]  (* A256664 *)

%Y Cf. A000045, A256655.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Apr 08 2015