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%I #8 Jul 03 2022 09:22:22
%S 53,82,214,321,336,472,541,4477
%N Maximum length of 3 finite snakes in the Snake Number Problem with n-periodic instructions in an infinite square grid (see Comments).
%C We start with 3 infinite snakes, and 4 possible directions: up, right, down, left.
%C 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.
%C The snakes can be blocked and finish there or can continue infinitely.
%C 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)?
%H Ariel Futoransky, <a href="http://snake.puzzlefun.online/">Snake Program</a>, Snake Program to try the snakes, April 2022 (to see more Snakes after the instruction you put :0 :0 for 3 snakes).
%H Rodolfo Kurchan, <a href="http://www.puzzlefun.online/problems">Puzzle Fun</a>, Snake Number Problem, March 2022.
%e | Instructions that give
%e n | Maximum length | the maximal length
%e --------------------------------------------
%e 4 53 URDL
%e 5 82 URDLU
%e 6 214 UURDUL
%e 7 321 URUULDU
%e 8 336 URURUULD
%e 9 472 URDDDDDDL
%e 10 541 UUURUDLLDD
%e 11 4477 UUDDRDUUUDL
%Y Cf. A353176, A353234.
%K nonn,more
%O 4,1
%A _Rodolfo Kurchan_, Jun 11 2022