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

%I A256664 #4 Apr 09 2015 07:58:50
%S A256664 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,
%T A256664 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,
%U A256664 35,34,36,35,34,39,37,36,35,21,21,21,21,22,21,23
%N A256664 Nonpositive part of the minimal alternating Fibonacci representation of n.
%C A256664 See A256655 for definitions.
%H A256664 Clark Kimberling, <a href="/A256664/b256664.txt">Table of n, a(n) for n = 0..1000</a>
%F A256664 A256663(n) - A256664(n) = n.
%e A256664 R(9) = 13 - 5 + 1, so that a(9) = 5.
%t A256664 b[n_] = Fibonacci[n]; bb = Table[b[n], {n, 1, 70}];
%t A256664 h[0] = {1}; h[n_] := Join[h[n - 1], Table[b[n + 2], {k, 1, b[n]}]];
%t A256664 g = h[23];  r[0] = {0};
%t A256664 r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
%t A256664 Table[Total[Abs[r[n]]], {n, 0, 100}] (* A256662 *)
%t A256664 Table[Total[(Abs[r[n]] + r[n])/2], {n, 0, 100}]  (* A256663 *)
%t A256664 Table[Total[(Abs[r[n]] - r[n])/2], {n, 0, 100}]  (* A256664 *)
%Y A256664 Cf. A000045, A256655, A256662, A256663.
%K A256664 nonn,easy
%O A256664 0,7
%A A256664 _Clark Kimberling_, Apr 08 2015