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