A256697 Trace of the minimal alternating triangular-number representation of n.

0, 1, -1, 3, 1, -1, 6, -3, 1, -1, 10, -1, -3, 1, -1, 15, 1, -1, -3, 1, -1, 21, -6, 1, -1, -3, 1, -1, 28, 3, -6, 1, -1, -3, 1, -1, 36, -1, 3, -6, 1, -1, -3, 1, -1, 45, 1, -1, 3, -6, 1, -1, -3, 1, -1, 55, -10, 1, -1, 3, -6, 1, -1, -3, 1, -1, 66, 1, -10, 1, -1

Offset: 0

Author

Clark Kimberling, Apr 11 2015

Keywords

• easy
• sign

Comments

See A255974 for definitions.

Examples

			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(8) = 10 - 3 + 1; trace = 1
R(11) = 15 - 6 + 3 - 1; trace = -1
		

References

• 0

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A255974, A256698, A256699.

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]]]
t = Table[r[n], {n, 0, 120}]  (* A255974 representations *)
t = Table[Last[r[n]], {n, 0, 120}] (* A256697 *)