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Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194844; an interspersion.
4

%I #5 Mar 30 2012 18:57:44

%S 1,2,3,4,5,6,7,8,9,10,12,13,14,15,11,17,19,20,21,16,18,23,25,27,28,22,

%T 24,26,30,32,34,36,29,31,33,35,39,41,43,45,38,40,42,44,37,48,51,53,55,

%U 47,50,52,54,46,49,58,61,64,66,57,60,63,65,56,59,62,69,72,75

%N Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194844; an interspersion.

%C See A194832 and A194844.

%e Northwest corner:

%e 1...2...4...7...12..17

%e 3...5...8...13..19..25

%e 6...9...14..20..27..34

%e 10..15..21..28..36..45

%e 11..16..22..29..38..47

%e 18..24..31..40..50..60

%t r = Sqrt[5];

%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}]] (* A194844 *)

%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},

%t {k, 1, n}]] (* A194845 *)

%t q[n_] := Position[p, n]; Flatten[

%t Table[q[n], {n, 1, 80}]] (* A194846 *)

%Y Cf. A194832, A194844, A194846.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Sep 04 2011