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A256759 Nonpositive part of the minimal alternating triangular-number representation of n (defined at A255974).

%I A256759 #4 Apr 13 2015 09:40:40
%S A256759 0,1,0,3,1,0,3,3,1,0,7,3,3,1,0,6,7,3,3,1,0,6,6,7,3,3,1,0,10,6,6,7,3,3,
%T A256759 1,0,11,10,6,6,7,3,3,1,0,10,11,10,6,6,7,3,3,1,0,10,10,11,10,6,6,7,3,3,
%U A256759 1,0,18,10,10,11,10,6,6,7,3,3,1,0,15,18
%N A256759 Nonpositive part of the minimal alternating triangular-number representation of n (defined at A255974).
%H A256759 Clark Kimberling, <a href="/A256759/b256759.txt">Table of n, a(n) for n = 1..1000</a>
%F A256759 A256700(n) - A256759(n) = n.
%e A256759 R(1) = 1; positive part 1, nonpositive part 0
%e A256759 R(2) = 3 - 1; positive part 3, nonpositive part 1
%e A256759 R(3) = 3; positive part 3, nonpositive part 0
%e A256759 R(11) = 15 - 6 + 3 - 1; positive part 15+3 = 18; nonpositive part 6 + 1 = 7
%t A256759 b[n_] := n (n + 1)/2; bb = Table[b[n], {n, 0, 1000}];
%t A256759 s[n_] := Table[b[n], {k, 1, n}];
%t A256759 h[1] = {1}; h[n_] := Join[h[n - 1], s[n]]; g = h[100]; r[0] = {0};
%t A256759 r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
%t A256759 Table[Total[(Abs[r[n]] + r[n])/2], {n, 1, 120}]  (* A256700 *)
%t A256759 Table[Total[(Abs[r[n]] - r[n])/2], {n, 1, 120}]  (* A256759 *)
%Y A256759 Cf. A255974, A256701.
%K A256759 nonn,easy
%O A256759 1,4
%A A256759 _Clark Kimberling_, Apr 13 2015