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

1,2

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A255974, A256759.

Sequence in context: A290418 A200690 A045773 * A175039 A222405 A146970

Adjacent sequences: A256697 A256698 A256699 * A256701 A256702 A256703

Keyword

nonn,easy

Author

Clark Kimberling, Apr 11 2015

Status

approved