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Challenge

Imagine a hexagonal grid as shown below. Let's call such a grid has size \$n\$ if it has \$n\$ dots on one side. The following is one of size 3:

  - - -
 - - - -
- - - - -
 - - - -
  - - -

Then, pick as many dots as possible on the grid so that no two dots are adjacent. For size 3, the maximum is 7 dots:

  - * -          * - *
 * - - *        - - - -
- - * - -  or  * - * - *
 * - - *        - - - -
  - * -          * - *

Your task is to output such a grid. For a size-\$n\$ hexagon, the output must contain exactly A002061(n) = \$n^2-n+1\$ non-adjacent dots. The corresponding maximal pattern can be found in this image linked on the OEIS sequence (imagine this: dissect all the hexagons there into triangles, remove one outermost layer of triangles, and pick the centers of original hexagons). The corresponding ASCII-art output must look like the following, modulo rotation/reflection:

n = 1
*

n = 2
 * - 
- - *
 * - 

n = 3 (following or alternative shown above)
  * - *  
 - - - - 
* - * - *
 - - - - 
  * - *  

n = 4
   * - - *   
  - - * - -  
 - * - - * - 
* - - * - - *
 - * - - * - 
  - - * - -  
   * - - *   

n = 5
    - * - - *    
   * - - * - -   
  - - * - - * -  
 - * - - * - - * 
* - - * - - * - -
 - * - - * - - * 
  - - * - - * -  
   * - - * - -   
    - * - - *    

n = 6
     - * - - * -     
    * - - * - - *    
   - - * - - * - -   
  - * - - * - - * -  
 * - - * - - * - - * 
- - * - - * - - * - -
 * - - * - - * - - * 
  - * - - * - - * -  
   - - * - - * - -   
    * - - * - - *    
     - * - - * -     

n = 7
      * - - * - - *      
     - - * - - * - -     
    - * - - * - - * -    
   * - - * - - * - - *   
  - - * - - * - - * - -  
 - * - - * - - * - - * - 
* - - * - - * - - * - - *
 - * - - * - - * - - * - 
  - - * - - * - - * - -  
   * - - * - - * - - *   
    - * - - * - - * -    
     - - * - - * - -     
      * - - * - - *      

n = 8
       - * - - * - - *       
      * - - * - - * - -      
     - - * - - * - - * -     
    - * - - * - - * - - *    
   * - - * - - * - - * - -   
  - - * - - * - - * - - * -  
 - * - - * - - * - - * - - * 
* - - * - - * - - * - - * - -
 - * - - * - - * - - * - - * 
  - - * - - * - - * - - * -  
   * - - * - - * - - * - -   
    - * - - * - - * - - *    
     - - * - - * - - * -     
      * - - * - - * - -      
       - * - - * - - *       

n = 9
        - * - - * - - * -        
       * - - * - - * - - *       
      - - * - - * - - * - -      
     - * - - * - - * - - * -     
    * - - * - - * - - * - - *    
   - - * - - * - - * - - * - -   
  - * - - * - - * - - * - - * -  
 * - - * - - * - - * - - * - - * 
- - * - - * - - * - - * - - * - -
 * - - * - - * - - * - - * - - * 
  - * - - * - - * - - * - - * -  
   - - * - - * - - * - - * - -   
    * - - * - - * - - * - - *    
     - * - - * - - * - - * -     
      - - * - - * - - * - -      
       * - - * - - * - - *       
        - * - - * - - * -        

n = 10
         * - - * - - * - - *         
        - - * - - * - - * - -        
       - * - - * - - * - - * -       
      * - - * - - * - - * - - *      
     - - * - - * - - * - - * - -     
    - * - - * - - * - - * - - * -    
   * - - * - - * - - * - - * - - *   
  - - * - - * - - * - - * - - * - -  
 - * - - * - - * - - * - - * - - * - 
* - - * - - * - - * - - * - - * - - *
 - * - - * - - * - - * - - * - - * - 
  - - * - - * - - * - - * - - * - -  
   * - - * - - * - - * - - * - - *   
    - * - - * - - * - - * - - * -    
     - - * - - * - - * - - * - -     
      * - - * - - * - - * - - *      
       - * - - * - - * - - * -       
        - - * - - * - - * - -        
         * - - * - - * - - *

I/O and rules

You can use any two distinct non-whitespace chars for marked and unmarked dots respectively. Trailing spaces on each line and leading/trailing whitespaces are allowed. Outputting a list of lines, and outputting integer charcodes instead of the corresponding chars are also allowed.

Standard rules apply. The shortest code in bytes wins.

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4 Answers 4

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5
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Charcoal, 33 bytes

ＮθＧ↙↘→→↗↖θ⎇﹪賓⟲∧ＬＶoIＧ；”“⟲∧⦄≧Σ¶ζ；

Try it online! Link is to verbose version of code. Explanation: After reading in n, the code simply draws a hexagon using one of two fill patterns depending on whether n is a multiple of 3; if it is, the fill pattern has the * one - in from the corner, otherwise it has the * in the top left corner.

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4
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Python 3.8 (pre-release), 92 bytes

f=lambda n,i=0:[l:=' '*(n-i)+('- * - '*n)[n%3%2+i<<1:][:n+i<<1]]+(n>i+1and[*f(n,i+1),l]or[])

Try it online!

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3
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Haskell, 84 bytes

f n=[[" * - -"!!mod(i+gcd 3n)6|i<-[1,3..2*y]++[4*y..2*y+4*n-4]]|y<-abs<$>[1-n..n-1]]

Try it online!

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2
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Jelly,  27  26 bytes

3ḍ6_BṙN€ṁ"Ḥ’rƊK€ṭ"Ḷ⁶ẋƊṚŒḄY

A full program that accepts a positive integer and prints using 0 as * and 1 as -.

Try it online! Or see a few with * and - in place of 0 and 1.

How?

3ḍ6_BṙN€ṁ"Ḥ’rƊK€ṭ"Ḷ⁶ẋƊṚŒḄY - Main Link: positive integer, n
3ḍ                         - three divides (n)? -> 1 if n is a multiple of three else 0
  6                        - six
   _                       - subtract -> 5 if n is a multiple of three else 6
    B                      - to binary -> 101 (i.e. "-*-") ...else 110 (i.e. "--*")
      N€                   - negate each (of implicit [1..n]) -> [-1,-2,...,-n]
     ṙ                     - rotate (110 or 101) left by (each of those) -> Patterns (one for each row of bottom half of a hexagon)
             Ɗ             - last three links as a monad, f(n):
          Ḥ                -   double -> 2n
           ’               -   decrement -> 2n-1
            r              -   (2n-1) inclusive range (n) -> [2n-1..n]
         "                 - zip (Patterns) and (range) applying, f(Pattern, i): 
        ṁ                  -   mould like -> resized rows using repetition
              K€           - join each with space characters -> Rows
                     Ɗ     - last three links as a monad, f(n):
                  Ḷ        -   lowered range -> [0..n-1]
                   ⁶       -   space character
                    ẋ      -   repeat -> leading spaces for bottom half
                 "         - zip (Rows) and (leading spaces) applying, f(row, spaces): 
                ṭ          -   tack (row) to (spaces)
                      Ṛ    - reverse -> top of the hexagon
                       ŒḄ  - bounce -> whole hexagon
                         Y - join with newline characters
                           - implicit, smashing print
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