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A194903 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194902; an interspersion.

%I A194903 #5 Mar 30 2012 18:57:44
%S A194903 1,3,2,5,4,6,9,7,10,8,13,11,14,12,15,19,16,20,17,21,18,25,22,26,23,27,
%T A194903 24,28,33,29,34,30,35,31,36,32,41,37,42,38,43,39,44,40,45,51,46,52,47,
%U A194903 53,48,54,49,55,50,61,56,62,57,63,58,64,59,65,60,66,73,67,74
%N A194903 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194902; an interspersion.
%C A194903 See A194832 for a general discussion.
%e A194903 Northwest corner:
%e A194903 1...3...5...9...13..19
%e A194903 2...4...7...11..16..22
%e A194903 6...10..14..20..26..34
%e A194903 8...12..17..23..30..38
%e A194903 15..21..27..35..43..53
%t A194903 r = -Sqrt[12];
%t A194903 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194903 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194903 Sort[t[n], Less]], {n, 1,
%t A194903     20}]] (* A194902 *)
%t A194903 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194903 Sort[t[n], Less]], {n, 1, 15}]]
%t A194903 row[n_] := Position[f, n];
%t A194903 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194903 g[n_, k_] := Part[row[n], k];
%t A194903 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194903 {k, 1, n}]] (* A194903 *)
%t A194903 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194903 {n, 1, 80}]]  (* A194904 *)
%Y A194903 Cf. A194832, A194902, A194903.
%K A194903 nonn,tabl
%O A194903 1,2
%A A194903 _Clark Kimberling_, Sep 05 2011