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Nonpositive part of the minimal alternating binary representation of n (defined at A256696).
3

%I #8 Apr 13 2015 09:40:34

%S 0,0,1,0,4,2,1,0,8,8,9,4,4,2,1,0,16,16,17,16,20,18,17,8,8,8,9,4,4,2,1,

%T 0,32,32,33,32,36,34,33,32,40,40,41,36,36,34,33,16,16,16,17,16,20,18,

%U 17,8,8,8,9,4,4,2,1,0,64,64,65,64,68,66,65,64,72

%N Nonpositive part of the minimal alternating binary representation of n (defined at A256696).

%H Clark Kimberling, <a href="/A256702/b256702.txt">Table of n, a(n) for n = 1..1000</a>

%F A256701(n) - A256702(n) = n.

%e R(1) = 1; positive part 1, nonpositive part 0.

%e R(2) = 2; positive part 2, nonpositive part 0.

%e R(3) = 4 - 1; positive part 4, nonpositive part 1.

%e R(11) = 16 - 8 + 4 - 1; positive part 16 + 4 = 20; nonpositive part 8 + 1 = 9.

%t b[n_] := 2^n; bb = Table[b[n], {n, 0, 40}];

%t s[n_] := Table[b[n + 1], {k, 1, b[n]}];

%t h[0] = {1}; h[n_] := Join[h[n - 1], s[n - 1]];

%t g = h[10]; Take[g, 100]; 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, 1, 100}] (* A073122 *)

%t u = Table[Total[(Abs[r[n]] + r[n])/2], {n, 1, 100}] (* A256701 *)

%t v = Table[Total[(Abs[r[n]] - r[n])/2], {n, 1, 100}] (* A256702 *)

%Y Cf. A256696, A073122, A256701.

%K nonn,easy

%O 1,5

%A _Clark Kimberling_, Apr 09 2015