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A194836 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194835; an interspersion.

%I A194836 #5 Mar 30 2012 18:57:44
%S A194836 1,3,2,5,4,6,9,7,10,8,13,11,14,12,15,19,16,20,17,21,18,26,23,27,24,28,
%T A194836 25,22,33,30,35,31,36,32,29,34,42,38,44,40,45,41,37,43,39,51,47,53,49,
%U A194836 55,50,46,52,48,54,62,57,64,59,66,61,56,63,58,65,60,74,69,76
%N A194836 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194835; an interspersion.
%C A194836 Each pair of rows eventually intersperse.
%e A194836  Northwest corner:
%e A194836 1...3...5...9...13..19..26
%e A194836 2...4...7...11..16..23..30
%e A194836 6...10..14..20..27..35..44
%e A194836 8...12..17..24..31..40..49
%e A194836 15..21..28..36..45..55..66
%e A194836 18..25..32..41..50..61..73
%t A194836 r = -Sqrt[2];
%t A194836 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194836 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 20}]]  (* A194835 *)
%t A194836 TableForm[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 15}]]
%t A194836 row[n_] := Position[f, n];
%t A194836 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194836 g[n_, k_] := Part[row[n], k];
%t A194836 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194836  {k, 1, n}]] (* A194836 *)
%t A194836 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194836  {n, 1, 80}]]  (* A194837 *)
%Y A194836 Cf. A194835, A194837, A194832.
%K A194836 nonn,tabl
%O A194836 1,2
%A A194836 _Clark Kimberling_, Sep 03 2011