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%I #8 Mar 30 2012 18:57:44
%S 1,2,1,3,2,1,3,2,1,4,3,2,5,1,4,3,6,2,5,1,4,7,3,6,2,5,1,4,7,3,6,2,5,1,
%T 8,4,7,3,6,2,9,5,1,8,4,7,3,10,6,2,9,5,1,8,4,11,7,3,10,6,2,9,5,1,8,4,
%U 11,7,3,10,6,2,9,5,1,12,8,4,11,7,3,10,6,2,13,9,5,1,12,8,4,11,7,3
%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=sqrt(3).
%C See A194832 for a general discussion.
%e First nine rows:
%e 1
%e 2 1
%e 3 2 1
%e 3 2 1 4
%e 3 2 5 1 4
%e 3 6 2 5 1 4
%e 7 3 6 2 5 1 4
%e 7 3 6 2 5 1 8 4
%e 7 3 6 2 9 5 1 8 4
%t r = Sqrt[3];
%t t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 20}]] (* A194838 *)
%t TableForm[Table[Flatten[(Position[t[n], #1] &) /@ 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}]] (* A194839 *)
%t q[n_] := Position[p, n]; Flatten[
%t Table[q[n], {n, 1, 80}]] (* A194840 *)
%Y Cf. A194832, A194839, A194840.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Sep 03 2011
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