A256699 Numbers with negative triangular trace.

2, 5, 7, 9, 11, 12, 14, 17, 18, 20, 22, 24, 25, 27, 30, 32, 33, 35, 37, 39, 41, 42, 44, 47, 49, 51, 52, 54, 56, 58, 60, 62, 63, 65, 68, 70, 72, 74, 75, 77, 81, 83, 85, 87, 88, 90, 92, 95, 97, 99, 101, 102, 104, 107, 110, 112, 114, 116, 117, 119, 121, 123

Offset

1,1

Comments

Are the differences all 1, 2, 3, or 4? 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, A256697, A256698 (complement)

Sequence in context: A077059 A260166 A007300 * A247421 A007069 A182463

Adjacent sequences: A256696 A256697 A256698 * A256700 A256701 A256702

Keyword

nonn,easy

Author

Clark Kimberling, Apr 11 2015

Status

approved