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A195111 Interspersion fractally induced by the fractal sequence A002260.

%I A195111 #6 Mar 30 2012 18:57:44
%S A195111 1,3,2,6,4,5,10,8,9,7,15,13,14,11,12,21,19,20,16,17,18,28,26,27,23,24,
%T A195111 25,22,36,34,35,31,32,33,29,30,45,43,44,40,41,42,37,38,39,55,53,54,50,
%U A195111 51,52,46,47,48,49,66,64,65,61,62,63,57,58,59,60,56,78,76,77
%N A195111 Interspersion fractally induced by the fractal sequence A002260.
%C A195111 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.
%C A195111 Every pair of rows eventually intersperse.  As a sequence, A194111 is a permutation of the positive integers, with inverse A195129.
%C A195111 The sequence A002260 is the fractal sequence obtained by concatenating the segments 1; 12; 123; 1234; 12345;...
%e A195111 Northwest corner:
%e A195111 1...3...6...10..15..21..28..36..45
%e A195111 2...4...8...13..19..26..34..43..53
%e A195111 5...9...14..20..27..35..44..54..65
%e A195111 7...11..16..23..31..40..50..61..73
%e A195111 12..17..24..32..41..51..62..74..87
%t A195111 j[n_] := Table[k, {k, 1, n}]; t[1] = j[1];
%t A195111 t[n_] := Join[t[n - 1], j[n]]   (* A002260 *)
%t A195111 t[12]
%t A195111 p[n_] := t[20][[n]]
%t A195111 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A195111 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A195111 f[20] (* A195110 *)
%t A195111 row[n_] := Position[f[30], n];
%t A195111 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A195111 v[n_, k_] := Part[row[n], k];
%t A195111 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A195111   {k, 1, n}]] (* A195111 *)
%t A195111 q[n_] := Position[w, n]; Flatten[Table[q[n],
%t A195111   {n, 1, 80}]]  (* A195112 *)
%Y A195111 Cf. A194959, A002260, A195110, A195112.
%K A195111 nonn,tabl
%O A195111 1,2
%A A195111 _Clark Kimberling_, Sep 09 2011