cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A352388 Number of solutions to Snake Number Problem for snakes with n-periodic instructions in an infinite square grid (see Comments).

Original entry on oeis.org

0, 0, 0, 0, 5, 21, 127, 618, 2934, 13542, 61803, 276650, 1219508, 5309179, 22868295, 97663066, 414156142, 1746438478
Offset: 1

Views

Author

Rodolfo Kurchan, Apr 29 2022

Keywords

Comments

Given a list of n move instructions (up, right, down, left), the snake starts at the origin and moves according to the instructions, in order. If an instruction tells it to move to a square that has already been visited, the snake skips that instruction. After it has followed (or skipped) the last instruction in the list, it starts again with the first one. a(n) is the number of lists of n instructions that results in the snake getting stuck at some point. Lists of instructions that are equivalent under rotations and reflections are counted only once, so we can for example assume that the first instruction is "up", and that the first "right" comes before the first "left". But how does one know when to interrupt a snake and deem it infinite? - Pontus von Brömssen, May 05 2022
Computer solutions a(5) to a(13) found by Giorgio Vecchi.
Computer solution a(14) to a(18) found by Ariel Futoransky.

Examples

			These are the 5 different solutions with 5 instructions:
UURDL: 19
  17 18  3  4 --
  16 19  2  5  6
  15 14  1  8  7
  -- 13 10  9 --
  -- 12 11 -- --
URDLL: 21
  -- 19 20 -- -- --
  17 18 21  2  3 --
  16 15 14  1  4  5
  -- 12 13  8  7  6
  -- 11 10  9 -- --
URRDL: 24
  -- -- 20 21 22
  17 18 19 24 23
  16 15  2  3  4
  13 14  1  6  5
  12 11  8  7 --
  -- 10  9 -- --
URDLU: 26
  -- -- 21 22 --
  16 17 20 23 24
  15 18 19 26 25
  14 13  2  3 --
  -- 12  1  4  5
  -- 11 10  7  6
  -- --  9  8 --
URDDL: 30
  -- -- 20 21 -- --
  -- 18 19 22 23 --
  16 17  2  3 24 --
  15 14  1  4 25 26
  12 13  6  5 30 27
  11 10  7 -- 29 28
  --  9  8 -- -- --

Links

  • Ariel Futoransky, Snake Program, Snake Program to try the snakes, April 2022 (see bottom animation and label for different options).
  • Rodolfo Kurchan, Puzzle Fun, Snake Number Problem, March 2022.

Crossrefs

Cf. A353259, A353060, A353176, A004147.

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

Original entry on oeis.org

53, 82, 214, 321, 336, 472, 541, 4477
Offset: 4

Views

Author

Rodolfo Kurchan, Jun 11 2022

Keywords

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.

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

Original entry on oeis.org

33, 75, 348, 435, 504, 595, 805, 4382
Offset: 4

Views

Author

Rodolfo Kurchan, Jun 11 2022

Keywords

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

Examples

			                      | 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

Links

  • 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.

Crossrefs

Cf. A353176, A353234, A354915.
Showing 1-3 of 3 results.

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