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A194877 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(8).

%I A194877 #5 Mar 30 2012 18:57:44
%S A194877 1,2,1,3,2,1,4,3,2,1,5,4,3,2,1,5,4,3,2,1,6,5,4,3,2,7,1,6,5,4,3,8,2,7,
%T A194877 1,6,5,4,9,3,8,2,7,1,6,5,10,4,9,3,8,2,7,1,6,11,5,10,4,9,3,8,2,7,1,6,
%U A194877 11,5,10,4,9,3,8,2,7,1,12,6,11,5,10,4,9,3,8,2,13,7,1,12,6,11,5,10
%N A194877 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(8).
%C A194877 See A194832 for a general discussion.
%e A194877 First nine rows:
%e A194877 1
%e A194877 2 1
%e A194877 3 2 1
%e A194877 4 3 2 1
%e A194877 5 4 3 2 1
%e A194877 5 4 3 2 1 6
%e A194877 5 4 3 2 7 1 6
%e A194877 5 4 3 8 2 7 1 6
%e A194877 5 4 9 3 8 2 7 1 6
%t A194877 r = Sqrt[8];
%t A194877 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194877 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194877 Sort[t[n], Less]], {n, 1, 20}]]   (* A194877 *)
%t A194877 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194877 Sort[t[n], Less]], {n, 1, 15}]]
%t A194877 row[n_] := Position[f, n];
%t A194877 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194877 g[n_, k_] := Part[row[n], k];
%t A194877 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194877 {k, 1, n}]]   (* A194878 *)
%t A194877 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194877 {n, 1, 80}]]   (* A194879 *)
%Y A194877 Cf. A194832, A194878, A194879.
%K A194877 nonn,tabl
%O A194877 1,2
%A A194877 _Clark Kimberling_, Sep 04 2011