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A194878 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194877; an interspersion.

%I A194878 #5 Mar 30 2012 18:57:44
%S A194878 1,3,2,6,5,4,10,9,8,7,15,14,13,12,11,20,19,18,17,16,21,27,25,24,23,22,
%T A194878 28,26,35,33,31,30,29,36,34,32,44,42,40,38,37,45,43,41,39,54,52,50,48,
%U A194878 46,55,53,51,49,47,65,63,61,59,57,66,64,62,60,58,56,76,74,72
%N A194878 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194877; an interspersion.
%C A194878 See A194832 for a general discussion.
%e A194878 Northwest corner:
%e A194878 1...3...6...10..15..20..27
%e A194878 2...5...9...14..19..25..33
%e A194878 4...8...13..18..24..31..40
%e A194878 7...12..17..23..30..38..48
%e A194878 11..16..22..29..37..46..57
%t A194878 r = Sqrt[8];
%t A194878 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194878 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194878 Sort[t[n], Less]], {n, 1, 20}]]   (* A194877 *)
%t A194878 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194878 Sort[t[n], Less]], {n, 1, 15}]]
%t A194878 row[n_] := Position[f, n];
%t A194878 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194878 g[n_, k_] := Part[row[n], k];
%t A194878 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194878 {k, 1, n}]]   (* A194878 *)
%t A194878 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194878 {n, 1, 80}]]   (* A194879 *)
%Y A194878 Cf. A194832, A194877, A194879.
%K A194878 nonn,tabl
%O A194878 1,2
%A A194878 _Clark Kimberling_, Sep 04 2011