|
%I #5 Mar 30 2012 18:57:44
%S 1,2,3,5,6,4,8,10,7,9,13,15,12,14,11,18,21,17,20,16,19,25,28,24,27,23,
%T 26,22,32,36,31,35,30,34,29,33,41,45,40,44,39,43,38,42,37,50,55,49,54,
%U 48,53,47,52,46,51,61,66,60,65,59,64,58,63,57,62,56,72,78,71
%N Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194899; an interspersion.
%C See A194832 for a general discussion.
%e Northwest corner:
%e 1...2...5...8...13..18
%e 3...6...10..15..21..28
%e 4...7...12..17..24..31
%e 9...14..20..27..35..44
%e 11..16..23..30..39..48
%t r = Sqrt[12];
%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}]] (* A194899 *)
%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, 15},
%t {k, 1, n}]] (* A194900 *)
%t q[n_] := Position[p, n]; Flatten[Table[q[n],
%t {n, 1, 90}]] (* A194901 *)
%Y Cf. A194832, A194899, A194901.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Sep 05 2011
|
