A256698 Numbers with positive triangular trace.

1, 3, 4, 6, 8, 10, 13, 15, 16, 19, 21, 23, 26, 28, 29, 31, 34, 36, 38, 40, 43, 45, 46, 48, 50, 53, 55, 57, 59, 61, 64, 66, 67, 69, 71, 73, 76, 78, 79, 80, 82, 84, 86, 89, 91, 93, 94, 96, 98, 100, 103, 105, 106, 108, 109, 111, 113, 115, 118, 120, 122, 124

Offset

1,2

Comments

Are the differences all 1, 2, or 3? See A255974 for definitions.

Links

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

Example

R(0) = 0; trace = 0
R(1) = 1; trace = 1
R(2) = 3 - 1; trace = -1
R(3) = 3; trace = 3
R(4) = 6 - 3 + 1; trace = 1
R(5) = 6 - 1; trace = -1
R(6) = 6; trace = 6
R(7) = 10 - 3; trace = -3
Thus, 1, 3, 4, 6, ... have positive trace, and 2, 5, 7, .... have negative trace.

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[Last[r[n]], {n, 0, 300}]   (* A256697 *)
Select[Range[200], Last[r[#]] > 0 &]  (* A256698 *)
Select[Range[200], Last[r[#]] < 0 &]  (* A256699 *)

Crossrefs

Cf. A255974, A256679, A256699 (complement).

Sequence in context: A059608 A088071 A247422 * A024182 A301752 A173339

Adjacent sequences: A256695 A256696 A256697 * A256699 A256700 A256701

Keyword

nonn,easy

Author

Clark Kimberling, Apr 11 2015

Status

approved