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A195114 Interspersion fractally induced by the fractal sequence obtained by deleting the second two terms of the fractal sequence A002260.

%I A195114 #5 Mar 30 2012 18:57:44
%S A195114 1,3,2,6,4,5,10,7,8,9,15,12,13,14,11,21,18,19,20,16,17,28,25,26,27,22,
%T A195114 23,24,36,33,34,35,29,30,31,32,45,42,43,44,38,39,40,41,37,55,52,53,54,
%U A195114 48,49,50,51,46,47,66,63,64,65,59,60,61,62,56,57,58,78,75,76
%N A195114 Interspersion fractally induced by the fractal sequence obtained by deleting the second two terms of the fractal sequence A002260.
%C A195114 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  Every pair of rows eventually intersperse.  As a sequence, A194114 is a permutation of the positive integers, with inverse A195115.
%e A195114 Northwest corner:
%e A195114 1...3...6...10..15..21..28
%e A195114 2...4...7...12..18..25..33
%e A195114 5...8...13..19..26..34..43
%e A195114 9...14..20..27..35..44..54
%e A195114 11..16..22..29..38..48..59
%t A195114 j[n_] := Table[k, {k, 1, n}];
%t A195114 t[1] = j[1]; t[2] = j[1];
%t A195114 t[n_] := Join[t[n - 1], j[n]] (* A002260; initial 1,1,2 repl by 1 *)
%t A195114 t[12]
%t A195114 p[n_] := t[20][[n]]
%t A195114 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A195114 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A195114 f[20]  (* A195113 *)
%t A195114 row[n_] := Position[f[30], n];
%t A195114 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A195114 v[n_, k_] := Part[row[n], k];
%t A195114 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A195114 {k, 1, n}]] (* A195114 *)
%t A195114 q[n_] := Position[w, n]; Flatten[Table[q[n],
%t A195114 {n, 1, 80}]]  (* A195115 *)
%Y A195114 Cf. A194959, A002260, A195113, A195115, A195111.
%K A195114 nonn,tabl
%O A195114 1,2
%A A195114 _Clark Kimberling_, Sep 09 2011