A194835 - OEIS

%I #5 Mar 30 2012 18:57:44

%S 1,2,1,2,1,3,2,4,1,3,2,4,1,3,5,2,4,6,1,3,5,7,2,4,6,1,3,5,7,2,4,6,1,8,

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

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

%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(2).

%C See A194832 for a general discussion.

%e First nine rows:

%e 1

%e 2 1

%e 2 1 3

%e 2 4 1 3

%e 2 4 1 3 5

%e 2 4 6 1 3 5

%e 7 2 4 6 1 3 5

%e 7 2 4 6 1 8 3 5

%e 7 2 9 4 6 1 8 3 5

%t r = -Sqrt[2];

%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}]]  (* A194835 *)

%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}]] (* A194836 *)

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

%t  {n, 1, 80}]]  (* A194837 *)

%Y Cf. A194832, A194836, A194837.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Sep 03 2011