A194897 - OEIS

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

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,16,23,25,26,27,28,

%T 22,24,30,32,34,35,36,29,31,33,38,40,42,44,45,37,39,41,43,47,49,51,53,

%U 55,46,48,50,52,54,57,59,61,63,65,56,58,60,62,64,66,69,71,73

%N Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194896; an interspersion.

%C See A194832 for a general discussion.

%e Northwest corner:

%e 1...2...4...7...11..17..23

%e 3...5...8...12..18..25..32

%e 6...9...13..19..26..34..42

%e 10..14..20..27..35..44..53

%e 15..21..28..36..45..55..65

%e 16..22..29..37..46..56..67

%t r = -Sqrt[8];

%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}]] (* A194896 *)

%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}]] (* A194897 *)

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

%t {n, 1, 80}]] (* A194898 *)

%Y Cf. A194832, A194896, A194898.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Sep 04 2011