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A194034 Natural interspersion of A028387, a rectangular array, by antidiagonals.

%I A194034 #6 Mar 30 2012 18:57:39
%S A194034 1,5,2,11,6,3,19,12,7,4,29,20,13,8,9,41,30,21,14,15,10,55,42,31,22,23,
%T A194034 16,17,71,56,43,32,33,24,25,18,89,72,57,44,45,34,35,26,27,109,90,73,
%U A194034 58,59,46,47,36,37,28,131,110,91,74,75,60,61,48,49,38,39,155,132
%N A194034 Natural interspersion of A028387, a rectangular array, by antidiagonals.
%C A194034 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, A194034 is a permutation of the positive integers; its inverse is A194035.
%e A194034 Northwest corner:
%e A194034 1...5...11...19...29...41
%e A194034 2...6...12...20...30...42
%e A194034 3...7...13...21...31...43
%e A194034 4...8...14...22...32...44
%e A194034 9...15..23...33...45...59
%t A194034 z = 30;
%t A194034 c[k_] := k^2 + k - 1;
%t A194034 c = Table[c[k], {k, 1, z}]  (* A028387 *)
%t A194034 f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t A194034 f = Table[f[n], {n, 1, 255}]  (* A074294 *)
%t A194034 r[n_] := Flatten[Position[f, n]]
%t A194034 t[n_, k_] := r[n][[k]]
%t A194034 TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
%t A194034 p = Flatten[Table[t[k, n - k + 1], {n, 1, 13}, {k, 1, n}]]  (* A194034 *)
%t A194034 q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]]  (* A194035 *)
%Y A194034 Cf. A194029, A194035.
%K A194034 nonn,tabl
%O A194034 1,2
%A A194034 _Clark Kimberling_, Aug 12 2011