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A194863 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194862; an interspersion.

%I A194863 #8 Jul 30 2023 03:44:42
%S A194863 1,2,3,5,6,4,8,10,7,9,12,14,11,13,15,18,20,16,19,21,17,24,27,22,25,28,
%T A194863 23,26,31,34,29,32,35,30,33,36,40,43,37,41,44,38,42,45,39,49,53,46,50,
%U A194863 54,47,51,55,48,52,60,64,57,61,65,58,62,66,59,63,56,71,76,68
%N A194863 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194862; an interspersion.
%C A194863 For a general discussion, see A194832.
%e A194863 Northwest corner:
%e A194863 1...2...5...8...12..18
%e A194863 3...6...10..14..20..27
%e A194863 4...7...11..16..22..29
%e A194863 9...13..19..25..32..41
%e A194863 15..21..28..35..44..54
%t A194863 r = (1 + Sqrt[3])/2;
%t A194863 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194863 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194863 Sort[t[n], Less]], {n, 1, 20}]]  (* A194862 *)
%t A194863 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194863 Sort[t[n], Less]], {n, 1, 15}]]
%t A194863 row[n_] := Position[f, n];
%t A194863 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194863 g[n_, k_] := Part[row[n], k];
%t A194863 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194863 {k, 1, n}]]  (* A194863 *)
%t A194863 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194863 {n, 1, 80}]]  (* A194867 *)
%Y A194863 Cf. A194832, A194862, A194867.
%K A194863 nonn,tabl
%O A194863 1,2
%A A194863 _Clark Kimberling_, Sep 04 2011