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