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A194909 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194905; an interspersion.

%I A194909 #5 Mar 30 2012 18:57:44
%S A194909 1,3,2,6,5,4,10,9,8,7,15,14,13,12,11,21,20,19,18,17,16,28,27,26,25,24,
%T A194909 23,22,35,34,33,32,31,30,29,36,44,42,41,40,39,38,37,45,43,54,52,50,49,
%U A194909 48,47,46,55,53,51,65,63,61,59,58,57,56,66,64,62,60,77,75,73
%N A194909 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194905; an interspersion.
%C A194909 See A194832 for a general discussion.
%e A194909 Northwest corner:
%e A194909 1...3...6...10..15..21
%e A194909 2...5...9...14..20..27
%e A194909 4...8...13..19..26..33
%e A194909 7...12..18..25..32..40
%e A194909 11..17..24..31..39..48
%e A194909 16..23..30..38..47..57
%t A194909 r = -Pi;
%t A194909 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194909 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194909 Sort[t[n], Less]], {n, 1, 20}]]  (* A194908 *)
%t A194909 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194909 Sort[t[n], Less]], {n, 1, 15}]]
%t A194909 row[n_] := Position[f, n];
%t A194909 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194909 g[n_, k_] := Part[row[n], k];
%t A194909 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194909 {k, 1, n}]]  (* A194909 *)
%t A194909 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194909 {n, 1, 80}]]  (* A194910 *)
%Y A194909 Cf. A194832, A194908, A194910.
%K A194909 nonn,tabl
%O A194909 1,2
%A A194909 _Clark Kimberling_, Sep 05 2011