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A194839 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194838; an interspersion.

%I A194839 #5 Mar 30 2012 18:57:44
%S A194839 1,3,2,6,5,4,9,8,7,10,14,12,11,15,13,20,18,16,21,19,17,27,25,23,28,26,
%T A194839 24,22,34,32,30,36,33,31,29,35,43,40,38,45,42,39,37,44,41,53,50,47,55,
%U A194839 52,49,46,54,51,48,64,61,58,66,63,60,57,65,62,59,56,75,72,69
%N A194839 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194838; an interspersion.
%C A194839 See A194832 and A194838.
%e A194839 Northwest corner:
%e A194839 1...3...6...9...14..20..27
%e A194839 2...5...8...12..18..25..32
%e A194839 4...7...11..16..23..30..38
%e A194839 10..15..21..28..36..45..55
%e A194839 13..19..26..33..42..52..63
%e A194839 17..24..31..39..49..60..71
%t A194839 r = Sqrt[3];
%t A194839 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194839 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 20}]]  (* A194838 *)
%t A194839 TableForm[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 15}]]
%t A194839 row[n_] := Position[f, n];
%t A194839 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194839 g[n_, k_] := Part[row[n], k];
%t A194839 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194839  {k, 1, n}]]  (* A194839 *)
%t A194839 q[n_] := Position[p, n]; Flatten[
%t A194839  Table[q[n], {n, 1, 80}]]  (* A194840 *)
%Y A194839 Cf. A194838, A194840, A194832.
%K A194839 nonn,tabl
%O A194839 1,2
%A A194839 _Clark Kimberling_, Sep 03 2011