|
%I #14 Apr 14 2022 11:19:36
%S 1,2,4,3,6,7,5,9,10,11,8,14,15,16,12,13,22,23,24,17,18,21,35,36,37,25,
%T 26,19,34,56,57,58,38,39,27,20,55,90,91,92,59,60,40,28,29,89,145,146,
%U 147,93,94,61,41,42,30,144,234,235,236,148,149,95,62,63,43,31
%N Natural interspersion of the Fibonacci sequence (1,2,3,5,8,...), 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, this sequence is a permutation of the positive integers; its inverse is A194031.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e Northwest corner:
%e 1...2...3...5...8...13
%e 4...6...9...14..22..35
%e 7...10..15..23..36..57
%e 11..16..24..37..58..92
%e 12..17..25..38..59..93
%t z = 40;
%t c[k_] := Fibonacci[k + 1];
%t c = Table[c[k], {k, 1, z}] (* A000045 *)
%t f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t f = Table[f[n], {n, 1, 800}] (* A194029 *)
%t r[n_] := Flatten[Position[f, n]]
%t t[n_, k_] := r[n][[k]]
%t TableForm[Table[t[n, k], {n, 1, 8}, {k, 1, 7}]]
%t p = Flatten[Table[t[k, n - k + 1], {n, 1, 13}, {k, 1, n}]] (* A194030 *)
%t q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A194031 *)
%Y Cf. A194029, A194031 (inverse).
%Y Column 1 appears to be A345347.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Aug 12 2011
|
