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A194988 Interspersion fractally induced by A194987, a rectangular array, by antidiagonals.

%I A194988 #13 Mar 30 2012 18:57:44
%S A194988 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 A194988 25,24,36,29,35,30,34,33,31,32,45,37,44,38,43,42,39,41,40,55,46,54,47,
%U A194988 53,52,48,51,49,50,66,56,65,57,64,63,58,62,59,61,60,78,67,77
%N A194988 Interspersion fractally induced by A194987, a rectangular array, by antidiagonals.
%C A194988 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 A194988 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A194988 Northwest corner:
%e A194988 1...3...6...10..15..21
%e A194988 2...4...7...11..16..22
%e A194988 5...9...14..20..27..35
%e A194988 8...12..17..23..30..38
%e A194988 13..19..26..34..43..53
%t A194988 r = Sqrt[6]; p[n_] := 1 + Floor[n/r]
%t A194988 Table[p[n], {n, 1, 90}] (* A194986 *)
%t A194988 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A194988 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A194988 f[20] (* A194987 *)
%t A194988 row[n_] := Position[f[30], n];
%t A194988 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A194988 v[n_, k_] := Part[row[n], k];
%t A194988 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A194988 {k, 1, n}]] (* A194988 *)
%t A194988 q[n_] := Position[w, n]; Flatten[Table[q[n],
%t A194988 {n, 1, 80}]]  (* A194989 *)
%Y A194988 Cf. A194959, A194986, A194988, A194989.
%K A194988 nonn,tabl
%O A194988 1,2
%A A194988 _Clark Kimberling_, Sep 07 2011