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A194984 Interspersion fractally induced by A194964, a rectangular array, by antidiagonals.

%I A194984 #5 Mar 30 2012 18:57:44
%S A194984 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 A194984 24,25,36,29,35,30,34,31,33,32,45,37,44,38,43,39,42,40,41,55,46,54,47,
%U A194984 53,48,52,49,51,50,66,56,65,57,64,58,63,59,62,61,60,78,67,77
%N A194984 Interspersion fractally induced by A194964, a rectangular array, by antidiagonals.
%C A194984 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  Every pair of rows eventually intersperse.  As a sequence, A194984 is a permutation of the positive integers, with inverse A194985.
%e A194984 Northwest corner:
%e A194984 1...3...6...10..15..21..28
%e A194984 2...4...7...11..16..22..29
%e A194984 5...9...14..20..27..35..44
%e A194984 8...12..17..23..30..38..47
%e A194984 13..19..26..34..43..53..64
%t A194984 r = Sqrt[5]; p[n_] := 1 + Floor[n/r]
%t A194984 Table[p[n], {n, 1, 90}]  (* A194964 *)
%t A194984 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A194984 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A194984 f[20] (* A194983 *)
%t A194984 row[n_] := Position[f[30], n];
%t A194984 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A194984 v[n_, k_] := Part[row[n], k];
%t A194984 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A194984 {k, 1, n}]]  (* A194984 *)
%t A194984 q[n_] := Position[w, n]; Flatten[Table[q[n],
%t A194984 {n, 1, 80}]]  (* A194985 *)
%Y A194984 Cf. A194959, A194964, A194983, A194985.
%K A194984 nonn,tabl
%O A194984 1,2
%A A194984 _Clark Kimberling_, Sep 07 2011