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A194911 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=2^(1/3).

%I A194911 #9 Mar 30 2012 18:57:44
%S A194911 1,1,2,1,2,3,4,1,2,3,4,1,5,2,3,4,1,5,2,6,3,4,1,5,2,6,3,7,4,8,1,5,2,6,
%T A194911 3,7,4,8,1,5,9,2,6,3,7,4,8,1,5,9,2,6,10,3,7,4,8,1,5,9,2,6,10,3,7,11,4,
%U A194911 8,12,1,5,9,2,6,10,3,7,11,4,8,12,1,5,9,13,2,6,10,3,7,11,4,8,12
%N A194911 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=2^(1/3).
%C A194911 See A194832 for a general discussion. The triangle is not equal to A194841.
%e A194911 First nine rows:
%e A194911 1
%e A194911 1 2
%e A194911 1 2 3
%e A194911 4 1 2 3
%e A194911 4 1 5 2 3
%e A194911 4 1 5 2 6 3
%e A194911 4 1 5 2 6 3 7
%e A194911 4 8 1 5 2 6 3 7
%e A194911 4 8 1 5 9 2 6 3 7
%t A194911 r = 2^(1/3);
%t A194911 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194911 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194911 Sort[t[n], Less]], {n, 1, 20}]]  (* A194911 *)
%t A194911 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194911 Sort[t[n], Less]], {n, 1, 15}]]
%t A194911 row[n_] := Position[f, n];
%t A194911 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194911 g[n_, k_] := Part[row[n], k];
%t A194911 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194911 {k, 1, n}]]  (* A194912 *)
%t A194911 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194911 {n, 1, 80}]]  (* A194913 *)
%Y A194911 Cf. A194832, A194912, A194913.
%K A194911 nonn,tabl
%O A194911 1,3
%A A194911 _Clark Kimberling_, Sep 05 2011