%I #13 Mar 30 2012 18:57:44

%S 1,3,2,6,4,5,10,7,9,8,15,11,14,12,13,21,16,20,17,19,18,28,22,27,23,26,

%T 25,24,36,29,35,30,34,33,31,32,45,37,44,38,43,42,39,41,40,55,46,54,47,

%U 53,52,48,51,49,50,66,56,65,57,64,63,58,62,59,61,60,78,67,77

%N Interspersion fractally induced by A194987, a rectangular array, by antidiagonals.

%C See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. Every pair of rows eventually intersperse. As a sequence, A194988 is a permutation of the positive integers, with inverse A194989.

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e Northwest corner:

%e 1...3...6...10..15..21

%e 2...4...7...11..16..22

%e 5...9...14..20..27..35

%e 8...12..17..23..30..38

%e 13..19..26..34..43..53

%t r = Sqrt[6]; p[n_] := 1 + Floor[n/r]

%t Table[p[n], {n, 1, 90}] (* A194986 *)

%t g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]

%t f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]

%t f[20] (* A194987 *)

%t row[n_] := Position[f[30], n];

%t u = TableForm[Table[row[n], {n, 1, 5}]]

%t v[n_, k_] := Part[row[n], k];

%t w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},

%t {k, 1, n}]] (* A194988 *)

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

%t {n, 1, 80}]] (* A194989 *)

%Y Cf. A194959, A194986, A194988, A194989.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Sep 07 2011