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A194902 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=-sqrt(12).

%I A194902 #5 Mar 30 2012 18:57:44
%S A194902 1,2,1,2,1,3,2,4,1,3,2,4,1,3,5,2,4,6,1,3,5,2,4,6,1,3,5,7,2,4,6,8,1,3,
%T A194902 5,7,2,4,6,8,1,3,5,7,9,2,4,6,8,10,1,3,5,7,9,2,4,6,8,10,1,3,5,7,9,11,2,
%U A194902 4,6,8,10,12,1,3,5,7,9,11,2,4,6,8,10,12,1,3,5,7,9,11,13,2,4,6
%N A194902 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=-sqrt(12).
%C A194902 See A194832 for a general discussion.
%e A194902 First nine rows:
%e A194902 1
%e A194902 2 1
%e A194902 2 1 3
%e A194902 2 4 1 3
%e A194902 2 4 6 1 3 5
%e A194902 2 4 6 1 3 5 7
%e A194902 2 4 6 8 1 3 5 7
%e A194902 2 4 6 8 1 3 5 7 9
%t A194902 r = -Sqrt[12];
%t A194902 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194902 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194902 Sort[t[n], Less]], {n, 1, 20}]] (* A194902 *)
%t A194902 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194902 Sort[t[n], Less]], {n, 1, 15}]]
%t A194902 row[n_] := Position[f, n];
%t A194902 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194902 g[n_, k_] := Part[row[n], k];
%t A194902 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194902 {k, 1, n}]] (* A194903 *)
%t A194902 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194902 {n, 1, 80}]]  (* A194904 *)
%Y A194902 Cf. A194832, A194903, A194904.
%K A194902 nonn,tabl
%O A194902 1,2
%A A194902 _Clark Kimberling_, Sep 05 2011