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A194874 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(6).

%I A194874 #5 Mar 30 2012 18:57:44
%S A194874 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 A194874 5,7,2,4,6,8,1,3,5,7,9,2,4,6,8,10,1,3,5,7,9,11,2,4,6,8,10,1,3,5,7,9,
%U A194874 11,2,4,6,8,10,1,12,3,5,7,9,11,2,13,4,6,8,10,1,12,3,5,7,9,11,2,13
%N A194874 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(6).
%C A194874 See A194832 for a general discussion.
%e A194874 First nine rows:
%e A194874 1
%e A194874 2 1
%e A194874 2 1 3
%e A194874 2 4 1 3
%e A194874 2 4 1 3 5
%e A194874 2 4 6 1 3 5
%e A194874 2 4 6 1 3 5 7
%e A194874 2 4 6 8 1 3 5 7
%e A194874 2 4 6 8 1 3 5 7 9
%t A194874 r = -Sqrt[6];
%t A194874 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194874 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194874 Sort[t[n], Less]], {n, 1, 20}]]   (* A194874 *)
%t A194874 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194874 Sort[t[n], Less]], {n, 1, 15}]]
%t A194874 row[n_] := Position[f, n];
%t A194874 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194874 g[n_, k_] := Part[row[n], k];
%t A194874 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194874 {k, 1, n}]]   (* A194875 *)
%t A194874 q[n_] := Position[p, n]; Flatten[
%t A194874 Table[q[n], {n, 1, 80}]]   (* A194876 *)
%Y A194874 Cf. A194832, A194875, A194876.
%K A194874 nonn,tabl
%O A194874 1,2
%A A194874 _Clark Kimberling_, Sep 04 2011