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%I #5 Mar 30 2012 18:57:44
%S 1,3,2,6,5,4,9,8,7,10,14,12,11,15,13,20,18,16,21,19,17,27,25,23,28,26,
%T 24,22,34,32,30,36,33,31,29,35,43,40,38,45,42,39,37,44,41,53,50,47,55,
%U 52,49,46,54,51,48,63,60,57,65,62,59,56,64,61,58,66,75,71,68
%N Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194859; an interspersion.
%C See A194832 for a general discussion.
%e Northwest corner:
%e 1...3...6...9...14..20
%e 2...5...8...12..18..25
%e 4...7...11..16..23..30
%e 10..15..21..28..36..45
%e 13..19..26..33..42..52
%e 17..24..31..39..49..59
%t r = E;
%t t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t Sort[t[n], Less]], {n, 1, 20}]] (* A194859 *)
%t TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t Sort[t[n], Less]], {n, 1, 15}]]
%t row[n_] := Position[f, n];
%t u = TableForm[Table[row[n], {n, 1, 20}]]
%t g[n_, k_] := Part[row[n], k];
%t p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t {k, 1, n}]] (* A194860 *)
%t q[n_] := Position[p, n]; Flatten[Table[q[n],
%t {n, 1, 80}]] (* A194861 *)
%Y Cf. A194859, A194861, A194832.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Sep 04 2011
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