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 A256699 Numbers with negative triangular trace. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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, A256679, 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

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Last modified February 21 09:51 EST 2024. Contains 370228 sequences. (Running on oeis4.)