A354915 Maximum length of 3 finite snakes in the Snake Number Problem with n-periodic instructions in an infinite square grid (see Comments).

53, 82, 214, 321, 336, 472, 541, 4477

Offset: 4

Author

Rodolfo Kurchan, Jun 11 2022

Keywords

• nonn
• more

Comments

We start with 3 infinite snakes, and 4 possible directions: up, right, down, left.

If on its turn one of the snakes cannot execute an order because that square is occupied, it goes to the next order, and so on.

The snakes can be blocked and finish there or can continue infinitely.

Which are the longest finite snakes using n instructions for 3 snakes that start in the same square (with n >= 4 because with 3 or fewer instructions are infinite)?

Examples

			                      | Instructions that give
   n | Maximum length |   the maximal length
  --------------------------------------------
   4          53              URDL
   5          82              URDLU
   6         214              UURDUL
   7         321              URUULDU
   8         336              URURUULD
   9         472              URDDDDDDL
  10         541              UUURUDLLDD
  11        4477              UUDDRDUUUDL
		

Links

• Ariel Futoransky, Snake Program, Snake Program to try the snakes, April 2022 (to see more Snakes after the instruction you put :0 :0 for 3 snakes).
• Rodolfo Kurchan, Puzzle Fun, Snake Number Problem, March 2022.

Crossrefs

Cf. A353176, A353234.