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A195108 Interspersion fractally induced by A004736.

%I A195108 #5 Mar 30 2012 18:57:44
%S A195108 1,2,3,5,6,4,8,10,7,9,13,15,11,14,12,19,21,17,20,18,16,26,28,23,27,24,
%T A195108 22,25,34,36,30,35,32,29,33,31,43,45,39,44,41,37,42,40,38,53,55,49,54,
%U A195108 51,47,52,50,48,46,64,66,59,65,62,57,63,61,58,56,60,76,78,71
%N A195108 Interspersion fractally induced by A004736.
%C A195108 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.
%C A195108 The sequence A004736 is the fractal sequence obtained by concatenating the segments 1; 2,1; 3,2,1; 4,3,2,1;...
%C A195108 Every pair of rows of A195108 eventually intersperse.
%C A195108 As a sequence, A194108 is a permutation of the positive integers, with inverse A195109.
%e A195108 Northwest corner:
%e A195108 1...2...5...8...13..19..26
%e A195108 3...6...10..15..21..28..36
%e A195108 4...7...11..17..23..30..39
%e A195108 9...14..20..27..35..44..54
%e A195108 12..18..24..32..41..51..62
%t A195108 j[n_] := Table[n + 1 - k, {k, 1, n}]; t[1] = j[1];
%t A195108 t[n_] := Join[t[n - 1], j[n]]   (* A004736 *)
%t A195108 t[10]
%t A195108 p[n_] := t[20][[n]]
%t A195108 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A195108 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A195108 f[20] (* A195107 *)
%t A195108 row[n_] := Position[f[30], n];
%t A195108 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A195108 v[n_, k_] := Part[row[n], k];
%t A195108 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A195108 {k, 1, n}]] (* A195108 *)
%t A195108 q[n_] := Position[w, n]; Flatten[Table[q[n],
%t A195108 {n, 1, 80}]] (* A195109 *)
%Y A195108 Cf. A194959, A004736, A195107, A195109.
%K A195108 nonn,tabl
%O A195108 1,2
%A A195108 _Clark Kimberling_, Sep 09 2011