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A256700 Positive part of the minimal alternating triangular-number representation of n (defined at A255974).

%I A256700 #4 Apr 13 2015 09:40:13
%S A256700 1,3,3,7,6,6,10,11,10,10,18,15,16,15,15,22,24,21,22,21,21,28,29,31,28,
%T A256700 29,28,28,39,36,37,39,36,37,36,36,48,48,45,46,48,45,46,45,45,56,58,58,
%U A256700 55,56,58,55,56,55,55,66,67,69,69,66,67,69,66,67,66,66
%N A256700 Positive part of the minimal alternating triangular-number representation of n (defined at A255974).
%H A256700 Clark Kimberling, <a href="/A256700/b256700.txt">Table of n, a(n) for n = 1..1000</a>
%F A256700 A256700(n) - A256759(n) = n.
%e A256700 R(1) = 1; positive part 1, nonpositive part 0
%e A256700 R(2) = 3 - 1; positive part 3, nonpositive part 1
%e A256700 R(3) = 3; positive part 3, nonpositive part 0
%e A256700 R(11) = 15 - 6 + 3 - 1; positive part 15+3 = 18; nonpositive part 6 + 1 = 7
%t A256700 b[n_] := n (n + 1)/2; bb = Table[b[n], {n, 0, 1000}];
%t A256700 s[n_] := Table[b[n], {k, 1, n}];
%t A256700 h[1] = {1}; h[n_] := Join[h[n - 1], s[n]]; g = h[100]; r[0] = {0};
%t A256700 r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
%t A256700 Table[Total[(Abs[r[n]] + r[n])/2], {n, 1, 120}]  (* A256700 *)
%t A256700 Table[Total[(Abs[r[n]] - r[n])/2], {n, 1, 120}]  (* A256759 *)
%Y A256700 Cf. A255974, A256759.
%K A256700 nonn,easy
%O A256700 1,2
%A A256700 _Clark Kimberling_, Apr 11 2015