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A194857 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194856; an interspersion.

%I A194857 #5 Mar 30 2012 18:57:44
%S A194857 1,3,2,6,5,4,10,9,8,7,14,13,12,11,15,20,18,17,16,21,19,27,25,23,22,28,
%T A194857 26,24,35,33,31,29,36,34,32,30,43,41,39,37,44,42,40,38,45,53,50,48,46,
%U A194857 54,51,49,47,55,52,64,61,58,56,65,62,59,57,66,63,60,76,73,70
%N A194857 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194856; an interspersion.
%C A194857 See A194832 for a general discussion.
%e A194857 Northwest corner:
%e A194857 1...3...6...10...14...20
%e A194857 2...5...9...13...18...25
%e A194857 4...8...12..17...23...51
%e A194857 7...11..16..22...29...37
%e A194857 15..21..38..36...44...54
%t A194857 r = -Sqrt[5];
%t A194857 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194857 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194857 Sort[t[n], Less]], {n, 1, 20}]]  (* A194856 *)
%t A194857 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194857 Sort[t[n], Less]], {n, 1, 15}]]
%t A194857 row[n_] := Position[f, n];
%t A194857 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194857 g[n_, k_] := Part[row[n], k];
%t A194857 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194857  {k, 1, n}]]  (* A194857 *)
%t A194857 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194857 {n, 1, 80}]]  (* A194858 *)
%Y A194857 Cf. A194856, A194858, A194832.
%K A194857 nonn,tabl
%O A194857 1,2
%A A194857 _Clark Kimberling_, Sep 04 2011