A195111 - OEIS

%I #6 Mar 30 2012 18:57:44

%S 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 25,22,36,34,35,31,32,33,29,30,45,43,44,40,41,42,37,38,39,55,53,54,50,

%U 51,52,46,47,48,49,66,64,65,61,62,63,57,58,59,60,56,78,76,77

%N Interspersion fractally induced by the fractal sequence A002260.

%C See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.

%C Every pair of rows eventually intersperse.  As a sequence, A194111 is a permutation of the positive integers, with inverse A195129.

%C The sequence A002260 is the fractal sequence obtained by concatenating the segments 1; 12; 123; 1234; 12345;...

%e Northwest corner:

%e 1...3...6...10..15..21..28..36..45

%e 2...4...8...13..19..26..34..43..53

%e 5...9...14..20..27..35..44..54..65

%e 7...11..16..23..31..40..50..61..73

%e 12..17..24..32..41..51..62..74..87

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

%t t[n_] := Join[t[n - 1], j[n]]   (* A002260 *)

%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] (* A195110 *)

%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}]] (* A195111 *)

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

%t   {n, 1, 80}]]  (* A195112 *)

%Y Cf. A194959, A002260, A195110, A195112.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Sep 09 2011