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A194835 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(2).

%I A194835 #5 Mar 30 2012 18:57:44
%S A194835 1,2,1,2,1,3,2,4,1,3,2,4,1,3,5,2,4,6,1,3,5,7,2,4,6,1,3,5,7,2,4,6,1,8,
%T A194835 3,5,7,2,9,4,6,1,8,3,5,7,2,9,4,6,1,8,3,10,5,7,2,9,4,11,6,1,8,3,10,5,
%U A194835 12,7,2,9,4,11,6,1,8,3,10,5,12,7,2,9,4,11,6,1,13,8,3,10,5,12,7,2
%N A194835 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(2).
%C A194835 See A194832 for a general discussion.
%e A194835 First nine rows:
%e A194835 1
%e A194835 2 1
%e A194835 2 1 3
%e A194835 2 4 1 3
%e A194835 2 4 1 3 5
%e A194835 2 4 6 1 3 5
%e A194835 7 2 4 6 1 3 5
%e A194835 7 2 4 6 1 8 3 5
%e A194835 7 2 9 4 6 1 8 3 5
%t A194835 r = -Sqrt[2];
%t A194835 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194835 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 20}]]  (* A194835 *)
%t A194835 TableForm[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 15}]]
%t A194835 row[n_] := Position[f, n];
%t A194835 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194835 g[n_, k_] := Part[row[n], k];
%t A194835 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194835  {k, 1, n}]] (* A194836 *)
%t A194835 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194835  {n, 1, 80}]]  (* A194837 *)
%Y A194835 Cf. A194832, A194836, A194837.
%K A194835 nonn,tabl
%O A194835 1,2
%A A194835 _Clark Kimberling_, Sep 03 2011