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A194908 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=-Pi. 4

%I

%S 1,2,1,3,2,1,4,3,2,1,5,4,3,2,1,6,5,4,3,2,1,7,6,5,4,3,2,1,7,6,5,4,3,2,

%T 1,8,7,6,5,4,3,2,9,1,8,7,6,5,4,3,10,2,9,1,8,7,6,5,4,11,3,10,2,9,1,8,7,

%U 6,5,12,4,11,3,10,2,9,1,8,7,6,13,5,12,4,11,3,10,2,9,1,8,7,14,6

%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=-Pi.

%C See A194832 for a general discussion.

%e First nine rows:

%e 1;

%e 2, 1;

%e 3, 2, 1;

%e 4, 3, 2, 1;

%e 5, 4, 3, 2, 1;

%e 6, 5, 4, 3, 2, 1;

%e 7, 6, 5, 4, 3, 2, 1;

%e 7, 6, 5, 4, 3, 2, 1, 8;

%e 7, 6, 5, 4, 3, 2, 9, 1, 8;

%t r = -Pi;

%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}]] (* A194908 *)

%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}]] (* A194909 *)

%t q[n_] := Position[p, n]; Flatten[Table[q[n],

%t {n, 1, 80}]] (* A194910 *)

%Y Cf. A194832, A194909, A194910.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Sep 05 2011

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Last modified October 20 03:04 EDT 2021. Contains 348099 sequences. (Running on oeis4.)