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A194872 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194871; an interspersion.

%I A194872 #8 Mar 30 2012 18:57:44
%S A194872 1,2,3,5,6,4,8,10,7,9,13,15,12,14,11,18,21,17,20,16,19,25,28,24,27,23,
%T A194872 26,22,32,36,31,35,30,34,29,33,41,45,40,44,39,43,38,42,37,50,55,49,54,
%U A194872 48,53,47,52,46,51,60,65,59,64,58,63,57,62,56,61,66,72,77,70
%N A194872 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194871; an interspersion.
%C A194872 See A194832 for a general discussion
%e A194872 Northwest corner:
%e A194872 1...2...5...8...13..18
%e A194872 3...6...10..15..21..28
%e A194872 4...7...12..17..24..31
%e A194872 9...14..20..27..35..44
%e A194872 11..16..23..30..39..48
%t A194872 r = Sqrt[6];
%t A194872 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194872 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194872 Sort[t[n], Less]], {n, 1, 20}]]   (* A194871 *)
%t A194872 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194872 Sort[t[n], Less]], {n, 1, 15}]]
%t A194872 row[n_] := Position[f, n];
%t A194872 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194872 g[n_, k_] := Part[row[n], k];
%t A194872 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194872 {k, 1, n}]]   (* A194872 *)
%t A194872 q[n_] := Position[p, n]; Flatten[
%t A194872 Table[q[n], {n, 1, 80}]]   (* A194873 *)
%Y A194872 Cf. A194832, A194872, A194873.
%K A194872 nonn,tabl
%O A194872 1,2
%A A194872 _Clark Kimberling_, Sep 04 2011