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A194918 Interspersion fractally induced by A189663, a rectangular array, by antidiagonals.

%I A194918 #5 Mar 30 2012 18:57:44
%S A194918 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 A194918 25,24,36,29,35,34,30,33,31,32,45,37,44,43,38,42,39,41,40,55,46,54,53,
%U A194918 47,52,48,51,50,49,66,56,65,64,57,63,58,62,61,59,60,78,67,77
%N A194918 Interspersion fractally induced by A189663, a rectangular array, by antidiagonals.
%C A194918 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  Every pair of rows eventually intersperse.  As a sequence, A194918 is a permutation of the positive integers, with inverse A194919.
%e A194918 Northwest corner:
%e A194918 1...3...6...10..15..21
%e A194918 2...4...7...11..16..22
%e A194918 5...9...14..20..27..35
%e A194918 8...13..19..26..34..43
%e A194918 12..17..23..30..38..47
%t A194918 r = GoldenRatio; p[n_] := n - Floor[n/r]
%t A194918 Table[p[n], {n, 1, 90}]  (* A189663 *)
%t A194918 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A194918 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A194918 f[20] (*  A194917 *)
%t A194918 row[n_] := Position[f[30], n];
%t A194918 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A194918 v[n_, k_] := Part[row[n], k];
%t A194918 w = Flatten[ Table[v[k, n - k + 1], {n, 1, 13},
%t A194918 {k, 1, n}]] (* A194918 *)
%t A194918 q[n_] := Position[w, n]; Flatten[Table[q[n],
%t A194918 {n, 1, 80}]] (* A194919 *)
%Y A194918 Cf. A194959, A189663, A194917, A194919.
%K A194918 nonn,tabl
%O A194918 1,2
%A A194918 _Clark Kimberling_, Sep 08 2011