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

%I A256663 #4 Apr 09 2015 08:03:07
%S A256663 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,
%T A256663 34,35,36,34,35,34,34,34,34,56,57,58,60,60,63,63,55,56,57,58,60,55,56,
%U A256663 57,55,56,55,55,55,55,90,91,92,94,94,97,97,97,103,102
%N A256663 Nonnegative part of the minimal alternating Fibonacci representation of n.
%C A256663 See A256655 for definitions.
%H A256663 Clark Kimberling, <a href="/A256663/b256663.txt">Table of n, a(n) for n = 0..1000</a>
%F A256663 A256663(n) - A256664(n) = n.
%e A256663 R(9) = 13 - 5 + 1, so that a(9) = 13 + 1 = 14.
%t A256663 b[n_] = Fibonacci[n]; bb = Table[b[n], {n, 1, 70}];
%t A256663 h[0] = {1}; h[n_] := Join[h[n - 1], Table[b[n + 2], {k, 1, b[n]}]];
%t A256663 g = h[23];
%t A256663 r[0] = {0}; r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
%t A256663 Table[Total[Abs[r[n]]], {n, 0, 100}] (* A256662 *)
%t A256663 Table[Total[(Abs[r[n]] + r[n])/2], {n, 0, 100}]  (* A256663 *)
%t A256663 Table[Total[(Abs[r[n]] - r[n])/2], {n, 0, 100}]  (* A256664 *)
%Y A256663 Cf. A000045, A256655, A256662, A256664.
%K A256663 nonn,easy
%O A256663 0,3
%A A256663 _Clark Kimberling_, Apr 08 2015