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

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, 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, 1, 0, 18, 10, 10, 11, 10, 6, 6, 7, 3, 3, 1, 0, 15, 18

Offset

1,4

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, A256701.

Sequence in context: A099546 A036870 A036874 * A336090 A255123 A244483

Adjacent sequences: A256756 A256757 A256758 * A256760 A256761 A256762

Keyword

nonn,easy

Author

Clark Kimberling, Apr 13 2015

Status

approved