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

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, 25, 18, 54, 55, 56, 57, 37, 38, 26, 19, 88, 89, 90, 91, 58, 59, 39, 27, 28, 143, 144, 145, 146, 92, 93, 60, 40, 41, 29, 232, 233, 234, 235, 147, 148, 94, 61, 62, 42, 30

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, A194056 is a permutation of the positive integers; its inverse is A194057.

Links

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

Example

Northwest corner:
1...2...4...7...12
3...5...8...13..21
6...9...14..22..35
10..15..23..36..57
11..16..24..37..58

Mathematica

z = 50;
c[k_] := -1 + Fibonacci[k + 2]
c = Table[c[k], {k, 1, z}] (* A000071, F(n+2)-1 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 300}]   (* 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, 11}, {k, 1, n}]] (* A194056 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]]  (* A194057 *)

Crossrefs

Cf. A194029, A194055, A000071, A000045, A194057.

Sequence in context: A228723 A247397 A194845 * A020753 A353888 A331162

Adjacent sequences: A194053 A194054 A194055 * A194057 A194058 A194059

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 13 2011

Status

approved