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

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, 24, 17, 87, 54, 55, 56, 36, 37, 25, 18, 142, 88, 89, 90, 57, 58, 38, 26, 27, 231, 143, 144, 145, 91, 92, 59, 39, 40, 28, 375, 232, 233, 234, 146, 147, 93, 60, 61, 41, 29

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, A194059 is a permutation of the positive integers; its inverse is A194060.

Links

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

Example

Northwest corner:
1...3...6...11...19
2...4...7...12...30
5...8...13..21...34
9...14..22..35...56
10..15..23..36...57

Mathematica

z = 50;
c[k_] := -2 + Fibonacci[k + 3];
c = Table[c[k], {k, 1, z}]  (* A001911, F(n+3)-2 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 700}]   (* cf. A194055 *)
r[n_] := Flatten[Position[f, n]]
t[n_, k_] := r[n][[k]]
TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
p = Flatten[Table[t[k, n - k + 1], {n, 1, 12}, {k, 1, n}]] (* A194059 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 100}]] (* A194060 *)

Crossrefs

Cf. A194029, A194059, A194062.

Sequence in context: A064789 A195111 A274315 * A191427 A191428 A191733

Adjacent sequences: A194056 A194057 A194058 * A194060 A194061 A194062

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 14 2011

Status

approved