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

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, 29, 28, 28, 39, 36, 37, 39, 36, 37, 36, 36, 48, 48, 45, 46, 48, 45, 46, 45, 45, 56, 58, 58, 55, 56, 58, 55, 56, 55, 55, 66, 67, 69, 69, 66, 67, 69, 66, 67, 66, 66

Offset: 1

Author

Clark Kimberling, Apr 11 2015

Keywords

• nonn
• easy

Examples

			R(1) = 1; positive part 1, nonpositive part 0
R(2) = 3 - 1; positive part 3, nonpositive part 1
R(3) = 3; positive part 3, nonpositive part 0
R(11) = 15 - 6 + 3 - 1; positive part 15+3 = 18; nonpositive part 6 + 1 = 7
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A255974, A256759.

Programs

Mathematica

b[n_] := n (n + 1)/2; bb = Table[b[n], {n, 0, 1000}];
s[n_] := Table[b[n], {k, 1, n}];
h[1] = {1}; h[n_] := Join[h[n - 1], s[n]]; g = h[100]; r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
Table[Total[(Abs[r[n]] + r[n])/2], {n, 1, 120}]  (* A256700 *)
Table[Total[(Abs[r[n]] - r[n])/2], {n, 1, 120}]  (* A256759 *)

Formula

A256700(n) - A256759(n) = n.