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A194030 Natural interspersion of the Fibonacci sequence (1,2,3,5,8,...), a rectangular array, by antidiagonals. 3
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, 26, 19, 34, 56, 57, 58, 38, 39, 27, 20, 55, 90, 91, 92, 59, 60, 40, 28, 29, 89, 145, 146, 147, 93, 94, 61, 41, 42, 30, 144, 234, 235, 236, 148, 149, 95, 62, 63, 43, 31 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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, A194030 is a permutation of the positive integers; its inverse is A194031.

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

Northwest corner:

1...2...3...5...8...13

4...6...9...14..22..35

7...10..15..23..36..57

11..16..24..37..58..92

12..17..25..38..59..93

MATHEMATICA

z = 40;

c[k_] := Fibonacci[k + 1];

c = Table[c[k], {k, 1, z}]  (* A000045 *)

f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]

f = Table[f[n], {n, 1, 800}]  (* A194029 *)

r[n_] := Flatten[Position[f, n]]

t[n_, k_] := r[n][[k]]

TableForm[Table[t[n, k], {n, 1, 8}, {k, 1, 7}]]

p = Flatten[Table[t[k, n - k + 1], {n, 1, 13}, {k, 1, n}]]  (* A194030 *)

q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194031 *)

CROSSREFS

Cf. A194029, A194031.

Sequence in context: A297551 A297673 A083050 * A083044 A126714 A035506

Adjacent sequences:  A194027 A194028 A194029 * A194031 A194032 A194033

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 12 2011

STATUS

approved

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Last modified October 22 09:57 EDT 2018. Contains 316433 sequences. (Running on oeis4.)