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A194059 Natural interspersion of A001911 (Fibonacci numbers minus 2); a rectangular array, by antidiagonals.

%I A194059 #5 Mar 30 2012 18:57:39
%S A194059 1,3,2,6,4,5,11,7,8,9,19,12,13,14,10,32,20,21,22,15,16,53,33,34,35,23,
%T A194059 24,17,87,54,55,56,36,37,25,18,142,88,89,90,57,58,38,26,27,231,143,
%U A194059 144,145,91,92,59,39,40,28,375,232,233,234,146,147,93,60,61,41,29
%N A194059 Natural interspersion of A001911 (Fibonacci numbers minus 2); a rectangular array, by antidiagonals.
%C A194059 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, A194059 is a permutation of the positive integers; its inverse is A194060.
%e A194059 Northwest corner:
%e A194059 1...3...6...11...19
%e A194059 2...4...7...12...30
%e A194059 5...8...13..21...34
%e A194059 9...14..22..35...56
%e A194059 10..15..23..36...57
%t A194059 z = 50;
%t A194059 c[k_] := -2 + Fibonacci[k + 3];
%t A194059 c = Table[c[k], {k, 1, z}]  (* A001911, F(n+3)-2 *)
%t A194059 f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t A194059 f = Table[f[n], {n, 1, 700}]   (* cf. A194055 *)
%t A194059 r[n_] := Flatten[Position[f, n]]
%t A194059 t[n_, k_] := r[n][[k]]
%t A194059 TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
%t A194059 p = Flatten[Table[t[k, n - k + 1], {n, 1, 12}, {k, 1, n}]] (* A194059 *)
%t A194059 q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 100}]] (* A194060 *)
%Y A194059 Cf. A194029, A194059, A194062.
%K A194059 nonn,tabl
%O A194059 1,2
%A A194059 _Clark Kimberling_, Aug 14 2011