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%I #6 Mar 30 2012 18:57:44
%S 1,2,3,5,6,4,8,10,7,9,12,14,11,13,15,18,20,16,19,21,17,24,27,22,25,28,
%T 23,26,32,35,30,33,36,31,34,29,40,44,38,42,45,39,43,37,41,49,53,47,51,
%U 55,48,52,46,50,54,60,64,57,62,66,59,63,56,61,65,58,71,76,68
%N Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194832; an interspersion.
%C As a sequence, A194833 is a permutation of the positive integers; its inverse is A194834.
%e Northwest corner:
%e 1...2...5...8...12..18..24
%e 3...6...10..14..20..27..35
%e 4...7...11..16..22..30..38
%e 9...13..19..25..33..42..51
%e 15..21..28..36..45..55..66
%t r = -GoldenRatio;
%t t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 20}]]
%t (* A194832 *)
%t TableForm[Table[Flatten[(Position[t[n], #1] &) /@ 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}, {k, 1, n}]] (* A194833 *)
%t q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A194834 *)
%Y Cf. A194832, A194834.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Sep 03 2011
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