A354916 Maximum length of 4 finite snakes in the Snake Number Problem with n-periodic instructions in an infinite square grid (see Comments).

33, 75, 348, 435, 504, 595, 805, 4382

Offset

4,1

Comments

We start with 4 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 4 snakes that start in the same square (with n >= 4 because with 3 or fewer instructions are infinite)?LINKS

Links

Table of n, a(n) for n=4..11.

Ariel Futoransky, Snake Program, Snake Program to try the snakes, April 2022 (to see more Snakes after the instruction you put :0 :0 :0 for 4 snakes).

Rodolfo Kurchan, Puzzle Fun, Snake Number Problem, March 2022.

Example

                      | Instructions that give
   n | Maximum length |   the maximal length
  --------------------------------------------
   4          33              URDL
   5          75              URDLU
   6         348              UURDUL
   7         435              URUULDU
   8         504              URURUULD
   9         595              URDDDDDDL
  10         805              UUURUDLLDD
  11        4382              UUDDRDUUUDL

Crossrefs

Cf. A353176, A353234, A354915.

Sequence in context: A240884 A049012 A137187 * A134037 A138841 A248979

Adjacent sequences: A354913 A354914 A354915 * A354917 A354918 A354919

Keyword

nonn,more

Author

Rodolfo Kurchan, Jun 11 2022

Status

approved