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A194067 Natural interspersion of A087483; a rectangular array, by antidiagonals.

%I A194067 #5 Mar 30 2012 18:57:39
%S A194067 1,2,3,4,5,8,6,7,11,12,9,10,15,16,21,13,14,19,20,26,27,17,18,24,25,32,
%T A194067 33,40,22,23,30,31,38,39,47,48,28,29,36,37,45,46,55,56,65,34,35,43,44,
%U A194067 53,54,63,64,74,75,41,42,51,52,61,62,72,73,84,85,96,49,50,59
%N A194067 Natural interspersion of A087483; a rectangular array, by antidiagonals.
%C A194067 See A194029 for definitions of natural fractal sequence and natural interspersion.  Every positive integer occurs exactly once (and every pair of rows intersperse), so that as a sequence, A194067 is a permutation of the positive integers; its inverse is A194068.
%e A194067 Northwest corner:
%e A194067 1...2...4...6...9...13
%e A194067 3...5...7...10..14..18
%e A194067 8...11..15..19..24..30
%e A194067 12..16..20..25..31..37
%e A194067 21..26..32..38..45..53
%t A194067 z = 70;
%t A194067 c[k_] := 1 + Floor[(1/3) k^2];
%t A194067 c = Table[c[k], {k, 1, z}]  (* A087483 *)
%t A194067 f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t A194067 f = Table[f[n], {n, 1, 300}]   (* A194066 *)
%t A194067 r[n_] := Flatten[Position[f, n]]
%t A194067 t[n_, k_] := r[n][[k]]
%t A194067 TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
%t A194067 p = Flatten[Table[t[k, n - k + 1], {n, 1, 14}, {k, 1, n}]] (* A194067 *)
%t A194067 q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]] (* A194068 *)
%Y A194067 Cf. A194029, A194066, A194068, A087483.
%K A194067 nonn,tabl
%O A194067 1,2
%A A194067 _Clark Kimberling_, Aug 14 2011