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A194842 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194841; an interspersion.

%I A194842 #5 Mar 30 2012 18:57:44
%S A194842 1,2,3,4,5,6,8,9,10,7,12,14,15,11,13,17,19,21,16,18,20,23,25,27,22,24,
%T A194842 26,28,31,33,35,29,32,34,36,30,39,42,44,37,40,43,45,38,41,48,51,54,46,
%U A194842 49,52,55,47,50,53,58,61,64,56,59,62,65,57,60,63,66,70,73,76
%N A194842 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194841; an interspersion.
%C A194842 See A194832 and A194841.
%e A194842 Northwest corner:
%e A194842 1...2...4...8...12..17..23
%e A194842 3...5...9...14..19..25..33
%e A194842 6...10..15..21..27..35..44
%e A194842 7...11..16..22..29..37..46
%e A194842 13..18..24..32..40..49..59
%t A194842 r = -Sqrt[3];
%t A194842 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194842 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1,20}]]   (* A194841 *)
%t A194842 TableForm[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 15}]]
%t A194842 row[n_] := Position[f, n];
%t A194842 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194842 g[n_, k_] := Part[row[n], k];
%t A194842 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194842  {k, 1, n}]]    (* A194842 *)
%t A194842 q[n_] := Position[p, n]; Flatten[
%t A194842  Table[q[n], {n, 1, 80}]]   (* A194843 *)
%Y A194842 Cf. A194841, A194843, A194832.
%K A194842 nonn,tabl
%O A194842 1,2
%A A194842 _Clark Kimberling_, Sep 04 2011