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

%I A256662 #4 Apr 09 2015 08:02:55
%S A256662 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 A256662 53,42,43,44,39,40,37,36,35,34,77,78,79,82,81,86,85,68,69,70,71,74,63,
%U A256662 64,65,60,61,58,57,56,55,124,125,126,129,128,133,132,131
%N A256662 Sum of absolute values of terms in the minimal alternating Fibonacci representation of n.
%C A256662 The terms are distinct.  See A256655 for definitions.
%H A256662 Clark Kimberling, <a href="/A256662/b256662.txt">Table of n, a(n) for n = 0..1000</a>
%e A256662 Minimal alternating Fibonacci representations:
%e A256662 R(0) = 0
%e A256662 R(1) = 1
%e A256662 R(2) = 2
%e A256662 R(3) = 3
%e A256662 R(4) = 5 - 1, so that a(4) = 6.
%e A256662 R(9) = 13 - 5 + 1, so that a(9) = 19.
%t A256662 b[n_] = Fibonacci[n]; bb = Table[b[n], {n, 1, 70}];
%t A256662 h[0] = {1}; h[n_] := Join[h[n - 1], Table[b[n + 2], {k, 1, b[n]}]];
%t A256662 g = h[23];  r[0] = {0};
%t A256662 r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
%t A256662 Table[Total[Abs[r[n]]], {n, 0, 100}] (* A256662 *)
%t A256662 Table[Total[(Abs[r[n]] + r[n])/2], {n, 0, 100}]  (* A256663 *)
%t A256662 Table[Total[(Abs[r[n]] - r[n])/2], {n, 0, 100}]  (* A256664 *)
%Y A256662 Cf. A000045, A256655.
%K A256662 nonn,easy
%O A256662 0,3
%A A256662 _Clark Kimberling_, Apr 08 2015