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A194915 Interspersion fractally induced by A194990, a rectangular array, by antidiagonals.

%I A194915 #5 Mar 30 2012 18:57:44
%S A194915 1,3,2,6,4,5,10,7,9,8,15,11,14,13,12,21,16,20,19,17,18,28,22,27,26,23,
%T A194915 25,24,36,29,35,34,30,33,32,31,45,37,44,43,38,42,41,39,40,55,46,54,53,
%U A194915 47,52,51,48,50,49,66,56,65,64,57,63,62,58,61,60,59,78,67,77
%N A194915 Interspersion fractally induced by A194990, a rectangular array, by antidiagonals.
%C A194915 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  Every pair of rows eventually intersperse.  As a sequence, A194915 is a permutation of the positive integers, with inverse A194916.
%e A194915 Northwest corner:
%e A194915 1...3...6...10..15..21
%e A194915 2...4...7...11..16..22
%e A194915 5...9...14..20..27..35
%e A194915 8...13..19..26..34..43
%e A194915 12..17..23..30..38..47
%t A194915 r = Sqrt[8]; p[n_] := 1 + Floor[n/r]
%t A194915 Table[p[n], {n, 1, 90}]  (* A194990  *)
%t A194915 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A194915 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A194915 f[20] (* A194914 *)
%t A194915 row[n_] := Position[f[30], n];
%t A194915 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A194915 v[n_, k_] := Part[row[n], k];
%t A194915 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A194915 {k, 1, n}]]  (* A194915 *)
%t A194915 q[n_] := Position[w, n]; Flatten[Table[q[n],
%t A194915 {n, 1, 80}]]  (* A194916 *)
%Y A194915 Cf. A194959, A194990, A194915, A194916.
%K A194915 nonn,tabl
%O A194915 1,2
%A A194915 _Clark Kimberling_, Sep 08 2011