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A194075 Natural interspersion of A194073; a rectangular array, by antidiagonals.

%I A194075 #5 Mar 30 2012 18:57:39
%S A194075 1,4,2,7,5,3,13,8,6,10,19,14,9,16,11,28,20,15,22,17,12,37,29,21,31,23,
%T A194075 18,25,49,38,30,40,32,24,34,26,61,50,39,52,41,33,43,35,27,76,62,51,64,
%U A194075 53,42,55,44,36,46,91,77,63,79,65,54,67,56,45,58,47,109,92,78
%N A194075 Natural interspersion of A194073; a rectangular array, by antidiagonals.
%C A194075 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, A194075 is a permutation of the positive integers; its inverse is A194076.
%e A194075 Northwest corner:
%e A194075 1...4...7...13...19
%e A194075 2...5...8...14...20
%e A194075 3...6...9...15...21
%e A194075 10..16..22..31...40
%e A194075 11..17..23..32...41
%t A194075 z = 70;
%t A194075 c[k_] := 1 + Floor[(3/4) k^2];
%t A194075 c = Table[c[k], {k, 1, z}]  (* A194073 *)
%t A194075 f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t A194075 f = Table[f[n], {n, 1, 300}]   (* A194074 *)
%t A194075 r[n_] := Flatten[Position[f, n]]
%t A194075 t[n_, k_] := r[n][[k]]
%t A194075 TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
%t A194075 p = Flatten[
%t A194075   Table[t[k, n - k + 1], {n, 1, 14}, {k, 1, n}]] (* A194075 *)
%t A194075 q[n_] := Position[p, n]; Flatten[
%t A194075  Table[q[n], {n, 1, 90}]]  (* A194076 *)
%Y A194075 Cf. A194029, A194074, A194073, A194076.
%K A194075 nonn,tabl
%O A194075 1,2
%A A194075 _Clark Kimberling_, Aug 14 2011