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A194866 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194865; an interspersion.

%I A194866 #8 Jul 30 2023 03:37:15
%S A194866 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 A194866 26,28,31,33,35,29,32,34,36,30,39,42,44,37,40,43,45,38,41,48,51,54,46,
%U A194866 49,52,55,47,50,53,59,62,65,57,60,63,66,58,61,64,56,70,74,77
%N A194866 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194865; an interspersion.
%e A194866 Northwest corner:
%e A194866 1...2...4...8...12..17..23
%e A194866 3...5...9...14..19..25..33
%e A194866 6...10..15..21..27..35..44
%e A194866 7...11..16..22..29..37..46
%e A194866 13..18..24..32..40..49..60
%t A194866 r = -E;
%t A194866 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194866 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194866 Sort[t[n], Less]], {n, 1, 20}]]  (* A194865 *)
%t A194866 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194866 Sort[t[n], Less]], {n, 1, 15}]]
%t A194866 row[n_] := Position[f, n];
%t A194866 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194866 g[n_, k_] := Part[row[n], k];
%t A194866 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194866 {k, 1, n}]]  (* A194866 *)
%t A194866 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194866 {n, 1, 80}]]  (* A194864 *)
%Y A194866 Cf. A194832, A194864, A194865.
%K A194866 nonn,tabl
%O A194866 1,2
%A A194866 _Clark Kimberling_, Sep 04 2011