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A194845 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194844; an interspersion.

%I A194845 #5 Mar 30 2012 18:57:44
%S A194845 1,2,3,4,5,6,7,8,9,10,12,13,14,15,11,17,19,20,21,16,18,23,25,27,28,22,
%T A194845 24,26,30,32,34,36,29,31,33,35,39,41,43,45,38,40,42,44,37,48,51,53,55,
%U A194845 47,50,52,54,46,49,58,61,64,66,57,60,63,65,56,59,62,69,72,75
%N A194845 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194844; an interspersion.
%C A194845 See A194832 and A194844.
%e A194845 Northwest corner:
%e A194845 1...2...4...7...12..17
%e A194845 3...5...8...13..19..25
%e A194845 6...9...14..20..27..34
%e A194845 10..15..21..28..36..45
%e A194845 11..16..22..29..38..47
%e A194845 18..24..31..40..50..60
%t A194845 r = Sqrt[5];
%t A194845 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194845 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 20}]]  (* A194844 *)
%t A194845 TableForm[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 15}]]
%t A194845 row[n_] := Position[f, n];
%t A194845 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194845 g[n_, k_] := Part[row[n], k];
%t A194845 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194845  {k, 1, n}]]    (* A194845 *)
%t A194845 q[n_] := Position[p, n]; Flatten[
%t A194845  Table[q[n], {n, 1, 80}]]   (* A194846 *)
%Y A194845 Cf. A194832, A194844, A194846.
%K A194845 nonn,tabl
%O A194845 1,2
%A A194845 _Clark Kimberling_, Sep 04 2011