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Interspersion fractally induced by the fractal sequence obtained by deleting the second two terms of the fractal sequence A002260.
3

%I #5 Mar 30 2012 18:57:44

%S 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 23,24,36,33,34,35,29,30,31,32,45,42,43,44,38,39,40,41,37,55,52,53,54,

%U 48,49,50,51,46,47,66,63,64,65,59,60,61,62,56,57,58,78,75,76

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

%C 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 Northwest corner:

%e 1...3...6...10..15..21..28

%e 2...4...7...12..18..25..33

%e 5...8...13..19..26..34..43

%e 9...14..20..27..35..44..54

%e 11..16..22..29..38..48..59

%t j[n_] := Table[k, {k, 1, n}];

%t t[1] = j[1]; t[2] = j[1];

%t t[n_] := Join[t[n - 1], j[n]] (* A002260; initial 1,1,2 repl by 1 *)

%t t[12]

%t p[n_] := t[20][[n]]

%t g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]

%t f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]

%t f[20] (* A195113 *)

%t row[n_] := Position[f[30], n];

%t u = TableForm[Table[row[n], {n, 1, 5}]]

%t v[n_, k_] := Part[row[n], k];

%t w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},

%t {k, 1, n}]] (* A195114 *)

%t q[n_] := Position[w, n]; Flatten[Table[q[n],

%t {n, 1, 80}]] (* A195115 *)

%Y Cf. A194959, A002260, A195113, A195115, A195111.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Sep 09 2011