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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 11 2015
STATUS
approved