A194863 - OEIS

%I #8 Jul 30 2023 03:44:42

%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 23,26,31,34,29,32,35,30,33,36,40,43,37,41,44,38,42,45,39,49,53,46,50,

%U 54,47,51,55,48,52,60,64,57,61,65,58,62,66,59,63,56,71,76,68

%N Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194862; an interspersion.

%C For a general discussion, see A194832.

%e Northwest corner:

%e 1...2...5...8...12..18

%e 3...6...10..14..20..27

%e 4...7...11..16..22..29

%e 9...13..19..25..32..41

%e 15..21..28..35..44..54

%t r = (1 + Sqrt[3])/2;

%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}]]  (* A194862 *)

%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}]]  (* A194863 *)

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

%t {n, 1, 80}]]  (* A194867 *)

%Y Cf. A194832, A194862, A194867.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Sep 04 2011