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A194906 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194905; an interspersion.

%I A194906 #5 Mar 30 2012 18:57:44
%S A194906 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T A194906 27,28,30,31,32,33,34,35,36,29,38,40,41,42,43,44,45,37,39,47,49,51,52,
%U A194906 53,54,55,46,48,50,57,59,61,63,64,65,66,56,58,60,62,68,70,72
%N A194906 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194905; an interspersion.
%C A194906 See A194832 for a general discussion.
%e A194906 Northwest corner:
%e A194906 1...2...4...7...11..16..22
%e A194906 3...5...8...12..17..23..31
%e A194906 6...9...13..18..24..32..41
%e A194906 10..14..19..25..33..42..52
%e A194906 15..20..26..34..43..53..64
%t A194906 r = Pi;
%t A194906 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194906 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194906 Sort[t[n], Less]], {n, 1, 20}]]  (* A194905 *)
%t A194906 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194906 Sort[t[n], Less]], {n, 1, 15}]]
%t A194906 row[n_] := Position[f, n];
%t A194906 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194906 g[n_, k_] := Part[row[n], k];
%t A194906 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194906 {k, 1, n}]]  (* A194906 *)
%t A194906 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194906 {n, 1, 80}]]  (* A194907 *)
%Y A194906 Cf. A194832, A194905, A194907.
%K A194906 nonn,tabl
%O A194906 1,2
%A A194906 _Clark Kimberling_, Sep 05 2011