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A194056 Natural interspersion of A000071(Fibonacci numbers minus 1), a rectangular array, by antidiagonals.

%I A194056 #5 Mar 30 2012 18:57:39
%S A194056 1,2,3,4,5,6,7,8,9,10,12,13,14,15,11,20,21,22,23,16,17,33,34,35,36,24,
%T A194056 25,18,54,55,56,57,37,38,26,19,88,89,90,91,58,59,39,27,28,143,144,145,
%U A194056 146,92,93,60,40,41,29,232,233,234,235,147,148,94,61,62,42,30
%N A194056 Natural interspersion of A000071(Fibonacci numbers minus 1), a rectangular array, by antidiagonals.
%C A194056 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, A194056 is a permutation of the positive integers; its inverse is A194057.
%e A194056 Northwest corner:
%e A194056 1...2...4...7...12
%e A194056 3...5...8...13..21
%e A194056 6...9...14..22..35
%e A194056 10..15..23..36..57
%e A194056 11..16..24..37..58
%t A194056 z = 50;
%t A194056 c[k_] := -1 + Fibonacci[k + 2]
%t A194056 c = Table[c[k], {k, 1, z}] (* A000071, F(n+2)-1 *)
%t A194056 f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t A194056 f = Table[f[n], {n, 1, 300}]   (* A194055 *)
%t A194056 r[n_] := Flatten[Position[f, n]]
%t A194056 t[n_, k_] := r[n][[k]]
%t A194056 TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
%t A194056 p = Flatten[Table[t[k, n - k + 1], {n, 1, 11}, {k, 1, n}]] (* A194056 *)
%t A194056 q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]]  (* A194057 *)
%Y A194056 Cf. A194029, A194055, A000071, A000045, A194057.
%K A194056 nonn,tabl
%O A194056 1,2
%A A194056 _Clark Kimberling_, Aug 13 2011