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

Author

Max Barrentine, Dec 06 2015

Keywords

• nonn
• tabl

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.

Examples

			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
		

Links

• Max Barrentine, Table of n, a(n) for n = 1..2484
• Alexis Monnerot-Dumaine, The Fibonacci Word fractal, HAL Id: hal-00367972, 2009.
• Alexis Monnerot-Dumaine, The Fibonacci word fractal [Cached copy, with permission]

Crossrefs

Cf. A332298, A332299.

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