A265318 Fibonacci word fractal in an n X n grid, starting downwards from the top-left corner, listed antidiagonally.

1, 0, 2, 5, 3, 0, 6, 4, 0, 0, 7, 0, 0, 0, 0, 0, 8, 10, 0, 0, 20, 0, 0, 9, 11, 0, 19, 21, 0, 0, 0, 0, 12, 18, 0, 22, 0, 0, 0, 0, 13, 0, 17, 23, 0, 0, 0, 0, 0, 0, 14, 16, 0, 24, 26, 0, 0, 0, 0, 0, 0, 15, 0, 0, 25, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 83

Offset

1,3

Comments

The n-th iteration of this curve ends at the n-th Fibonacci number.

As this is not a space-filling curve, not all points on the grid are reached by the curve; these points are given the value 0.

Links

Max Barrentine, Table of n, a(n) for n = 1..2484

Alexis Monnerot-Dumaine, The Fibonacci Word fractal, HAL Id: hal-00367972, 2009.

Example

The top left corner of the array shows how this curve begins (connect the terms in numerical order):
   1   0   5   6   7
   2   3   4   0   8
   0   0   0  10   9
   0   0   0  11   0
   0   0   0  12  13
  20  19  18   0  14
  21   0  17  16  15
  22  23   0   0   0
   0  24   0   0   0
  26  25   0   0   0
  27   0  31  32  33
  28  29  30   0  34

Crossrefs

Cf. A332298, A332299.

See also A163357, A163334, and A054238 for other fractal curves.

Sequence in context: A102892 A132898 A365728 * A279536 A269954 A326953

Adjacent sequences: A265315 A265316 A265317 * A265319 A265320 A265321

Keyword

nonn,tabl

Author

Max Barrentine, Dec 06 2015

Status

approved