cp's OEIS Frontend

A194896 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 A194896 #6 Mar 30 2012 18:57:44
%S A194896 1,1,2,1,2,3,1,2,3,4,1,2,3,4,5,6,1,2,3,4,5,6,1,7,2,3,4,5,6,1,7,2,8,3,
%T A194896 4,5,6,1,7,2,8,3,9,4,5,6,1,7,2,8,3,9,4,10,5,6,1,7,2,8,3,9,4,10,5,11,6,
%U A194896 12,1,7,2,8,3,9,4,10,5,11,6,12,1,7,13,2,8,3,9,4,10,5,11,6,12,1,7
%N A194896 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 A194896 See A194832 for a general discussion.
%e A194896 First nine rows:
%e A194896 1
%e A194896 1 2
%e A194896 1 2 3
%e A194896 1 2 3 4
%e A194896 1 2 3 4 5
%e A194896 6 1 2 3 4 5
%e A194896 6 1 7 2 3 4 5
%e A194896 6 1 7 2 8 3 4 5
%e A194896 6 1 7 2 8 3 9 4 5
%t A194896 r = -Sqrt[8];
%t A194896 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194896 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194896 Sort[t[n], Less]], {n, 1, 20}]] (* A194896 *)
%t A194896 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194896 Sort[t[n], Less]], {n, 1, 15}]]
%t A194896 row[n_] := Position[f, n];
%t A194896 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194896 g[n_, k_] := Part[row[n], k];
%t A194896 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194896 {k, 1, n}]] (* A194897 *)
%t A194896 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194896 {n, 1, 80}]] (* A194898 *)
%Y A194896 Cf. A194832, A194897, A194898.
%K A194896 nonn,tabl
%O A194896 1,3
%A A194896 _Clark Kimberling_, Sep 04 2011