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A256698
Numbers with positive triangular trace.
3
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
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, A256699 (complement).
Sequence in context: A059608 A088071 A247422 * A024182 A301752 A173339
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 11 2015
STATUS
approved