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A194897 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194896; an interspersion.

%I A194897 #5 Mar 30 2012 18:57:44
%S A194897 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,16,23,25,26,27,28,
%T A194897 22,24,30,32,34,35,36,29,31,33,38,40,42,44,45,37,39,41,43,47,49,51,53,
%U A194897 55,46,48,50,52,54,57,59,61,63,65,56,58,60,62,64,66,69,71,73
%N A194897 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194896; an interspersion.
%C A194897 See A194832 for a general discussion.
%e A194897 Northwest corner:
%e A194897 1...2...4...7...11..17..23
%e A194897 3...5...8...12..18..25..32
%e A194897 6...9...13..19..26..34..42
%e A194897 10..14..20..27..35..44..53
%e A194897 15..21..28..36..45..55..65
%e A194897 16..22..29..37..46..56..67
%t A194897 r = -Sqrt[8];
%t A194897 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194897 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194897 Sort[t[n], Less]], {n, 1, 20}]] (* A194896 *)
%t A194897 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194897 Sort[t[n], Less]], {n, 1, 15}]]
%t A194897 row[n_] := Position[f, n];
%t A194897 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194897 g[n_, k_] := Part[row[n], k];
%t A194897 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194897 {k, 1, n}]] (* A194897 *)
%t A194897 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194897 {n, 1, 80}]] (* A194898 *)
%Y A194897 Cf. A194832, A194896, A194898.
%K A194897 nonn,tabl
%O A194897 1,2
%A A194897 _Clark Kimberling_, Sep 04 2011