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A194912 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194905; an interspersion.

%I A194912 #5 Mar 30 2012 18:57:44
%S A194912 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 A194912 26,28,31,33,35,29,32,34,36,30,39,42,44,37,40,43,45,38,41,48,51,54,46,
%U A194912 49,52,55,47,50,53,58,61,64,56,59,62,65,57,60,63,66,70,73,76
%N A194912 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194905; an interspersion.
%C A194912 See A194832 for a general discussion.  A194912 is not equal to A194842.
%e A194912 Northwest corner:
%e A194912 1...2...4...8...12..17
%e A194912 3...5...9...14..19..25
%e A194912 6...10..15..21..27..35
%e A194912 7...11..16..22..29..37
%e A194912 13..18..24..32..40..49
%t A194912 r = 2^(1/3);
%t A194912 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194912 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194912 Sort[t[n], Less]], {n, 1, 20}]]  (* A194911 *)
%t A194912 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194912 Sort[t[n], Less]], {n, 1, 15}]]
%t A194912 row[n_] := Position[f, n];
%t A194912 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194912 g[n_, k_] := Part[row[n], k];
%t A194912 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194912 {k, 1, n}]]  (* A194912 *)
%t A194912 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194912 {n, 1, 80}]]  (* A194913 *)
%Y A194912 Cf. A194832, A194911, A194913.
%K A194912 nonn,tabl
%O A194912 1,2
%A A194912 _Clark Kimberling_, Sep 05 2011