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A194868 Triangular array (and fractal sequence): row n is the permutation of (1,2,...,n) obtained from the increasing ordering of fractional parts {r}, {2r}, ..., {nr}, where r=-(1+sqrt(3))/2.

%I A194868 #8 May 11 2013 08:11:34
%S A194868 1,2,1,2,1,3,2,4,1,3,5,2,4,1,3,5,2,4,1,6,3,5,2,7,4,1,6,3,8,5,2,7,4,1,
%T A194868 6,3,8,5,2,7,4,1,9,6,3,8,5,2,10,7,4,1,9,6,3,8,5,2,10,7,4,1,9,6,3,11,8,
%U A194868 5,2,10,7,4,12,1,9,6,3,11,8,5,13,2,10,7,4,12,1,9,6,3,11,8,5,13
%N A194868 Triangular array (and fractal sequence):  row n is the permutation of (1,2,...,n) obtained from the increasing ordering of fractional parts {r}, {2r}, ..., {nr}, where r=-(1+sqrt(3))/2.
%C A194868 See A194832 for a general discussion.
%e A194868 First nine rows:
%e A194868 1
%e A194868 2 1
%e A194868 2 1 3
%e A194868 2 4 1 3
%e A194868 5 2 4 1 3
%e A194868 5 2 4 1 6 3
%e A194868 5 2 7 4 1 6 3
%e A194868 8 5 2 7 4 1 6 3
%e A194868 8 5 2 7 4 1 9 6 3
%t A194868 r = -(1 + Sqrt[3])/2;
%t A194868 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194868 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194868 Sort[t[n], Less]], {n, 1, 20}]]  (* A194868 *)
%t A194868 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194868 Sort[t[n], Less]], {n, 1, 15}]]
%t A194868 row[n_] := Position[f, n];
%t A194868 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194868 g[n_, k_] := Part[row[n], k];
%t A194868 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194868 {k, 1, n}]] (* A194869 *)
%t A194868 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194868 {n, 1, 80}]]   (* A194870 *)
%Y A194868 Cf. A194832, A194869, A194870.
%K A194868 nonn,tabl
%O A194868 1,2
%A A194868 _Clark Kimberling_, Sep 04 2011