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A195074 Interspersion fractally induced by A194920, a rectangular array, by antidiagonals.

%I A195074 #6 Mar 30 2012 18:57:44
%S A195074 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 A195074 25,24,36,29,35,30,34,33,31,32,45,37,44,38,43,42,39,41,40,55,46,54,47,
%U A195074 53,52,48,51,49,50,66,56,65,57,64,63,58,62,59,61,60,78,67,77
%N A195074 Interspersion fractally induced by A194920, a rectangular array, by antidiagonals.
%C A195074 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  Every pair of rows eventually intersperse.  As a sequence, A194974 is a permutation of the positive integers, with inverse A195075.
%C A195074 To see that A195074 differs from A194988, note that the generating sequences A195072 and A194986 differ.
%e A195074 Northwest corner:
%e A195074 1...3...6...10..15..21
%e A195074 2...4...7...11..16..22
%e A195074 5...9...14..20..27..35
%e A195074 8...12..17..23..30..38
%e A195074 13..19..26..34..43..53
%t A195074 r = Sqrt[3]; p[n_] := n - Floor[n/r]
%t A195074 Table[p[n], {n, 1, 90}]   (* A195072 *)
%t A195074 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A195074 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A195074 f[20]   (* A195073 *)
%t A195074 row[n_] := Position[f[30], n];
%t A195074 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A195074 v[n_, k_] := Part[row[n], k];
%t A195074 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A195074 {k, 1, n}]]    (* A195074 *)
%t A195074 q[n_] := Position[w, n]; Flatten[
%t A195074 Table[q[n], {n, 1, 80}]]   (* A195075 *)
%Y A195074 Cf. A195072, A195074, A195075.
%K A195074 nonn,tabl
%O A195074 1,2
%A A195074 _Clark Kimberling_, Sep 08 2011