A346265
                                                                                                                            Aug 24 2021
                                                                                                                          Bernard Schott 
                                                       A346265(4) = 5.                            

Drawings of the five squares 30 X 30 that are tiled with squares of two different sizes so that the numbers of large or small squares are equal.

Notation: s = side of the tiled square, a = side of small squares, b = side of large squares, 
          z = number of small squares = number of large squares.

  1) Three squares 30 X 30 with distinct tilings of Type 1 (see A344331)
         
                                   ______ ______ ______ _ ______ ______ ______ _ ______ ______ ______ _         
                                  |      |      |      |_|      |      |      |_|      |      |      |_|       
                                  |      |      |      |_|      |      |      |_|      |      |      |_|       
                                  |______|______|______|_|______|______|______|_|______|______|______|_|         
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |______|_____ |______|_|______|______|______|_|______|______|______|_|               
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |______|______|______|_|______|______|______|_|______|______|______|_|
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |______|______|______|_|______|______|______|_|______|______|______|_|
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |______|______|______|_|______|______|______|_|______|______|______|_|
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |______|______|______|_|______|______|______|_|______|______|______|_|
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |______|______|______|_|______|______|______|_|______|______|______|_|
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |______|______|______|_|______|______|______|_|______|______|______|_|
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |______|______|______|_|______|______|______|_|______|______|______|_|
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |      |      |      |_|      |      |      |_|      |      |      |_|
                                  |______|______|______|_|______|______|______|_|______|______|______|_|


                                                       Square 30 X 30, type 1
                                                        a=1, b=3, s=30, z=90
                                                      Primitive square 30 X 30

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


                                ____ ____ _ ____ ____ _ ____ ____ _ ____ ____ _ ____ ____ _ ____ ____ _
                               |    |    |_|    |    |_|    |    |_|    |    |_|    |    |_|    |    |_| 
                               |____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|
                               |    |    |_|    |    |_|    |    |_|    |    |_|    |    |_|    |    |_| 
                               |____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|
                               |    |    |_|    |    |_|    |    |_|    |    |_|    |    |_|    |    |_| 
                               |____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|
                               |    |    |_|    |    |_|    |    |_|    |    |_|    |    |_|    |    |_| 
                               |____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|
                               |    |    |_|    |    |_|    |    |_|    |    |_|    |    |_|    |    |_| 
                               |____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|
                               |    |    |_|    |    |_|    |    |_|    |    |_|    |    |_|    |    |_| 
                               |____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|
                               |    |    |_|    |    |_|    |    |_|    |    |_|    |    |_|    |    |_| 
                               |____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|
                               |    |    |_|    |    |_|    |    |_|    |    |_|    |    |_|    |    |_| 
                               |____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|
                               |    |    |_|    |    |_|    |    |_|    |    |_|    |    |_|    |    |_| 
                               |____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|
                               |    |    |_|    |    |_|    |    |_|    |    |_|    |    |_|    |    |_| 
                               |____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|
                               |    |    |_|    |    |_|    |    |_|    |    |_|    |    |_|    |    |_| 
                               |____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|
                               |    |    |_|    |    |_|    |    |_|    |    |_|    |    |_|    |    |_| 
                               |____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|
                               |    |    |_|    |    |_|    |    |_|    |    |_|    |    |_|    |    |_| 
                               |____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|
                               |    |    |_|    |    |_|    |    |_|    |    |_|    |    |_|    |    |_| 
                               |____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|
                               |    |    |_|    |    |_|    |    |_|    |    |_|    |    |_|    |    |_| 
                               |____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|____|____|_|

                       
                                                         Square 30 X 30, type 1
                                                          a=1, b=2, s=30, z=180
                                              9 copies of primitive square 10 X 10 with z=20 

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

                               _____________ _____________ ______ _____________ _____________ ______
                              |             |             |      |             |             |      |
                              |             |             |      |             |             |      |
                              |             |             |______|             |             |______|
                              |             |             |      |             |             |      |
                              |             |             |      |             |             |      |
                              |_____________|_____________|______|_____________|_____________|______|     
                              |             |             |      |             |             |      |
                              |             |             |      |             |             |      |
                              |             |             |______|             |             |______|
                              |             |             |      |             |             |      |
                              |             |             |      |             |             |      |
                              |_____________|_____________|______|_____________|_____________|______|
                              |             |             |      |             |             |      |
                              |             |             |      |             |             |      |
                              |             |             |______|             |             |______|
                              |             |             |      |             |             |      |
                              |             |             |      |             |             |      |
                              |_____________|_____________|______|_____________|_____________|______|                                                    
                              |             |             |      |             |             |      |
                              |             |             |      |             |             |      |
                              |             |             |______|             |             |______|
                              |             |             |      |             |             |      |
                              |             |             |      |             |             |      |
                              |_____________|_____________|______|_____________|_____________|______|              
                              |             |             |      |             |             |      |
                              |             |             |      |             |             |      |
                              |             |             |______|             |             |______|
                              |             |             |      |             |             |      |
                              |             |             |      |             |             |      |
                              |_____________|_____________|______|_____________|_____________|______|

                           
                                                    Square 30 X 30, type 1
                                                     a=3, b=6, s=30, z=20
                                              Elementary square 30 X 30 with z=20
 
                  ---------------------------------------------------------------------------------------------------
                  ---------------------------------------------------------------------------------------------------
                  ---------------------------------------------------------------------------------------------------


    2) Two squares 30 X 30 with distinct tilings of Type 2 (see A344332)

          

                                   ________ ________ ________ ______ ________ ________ ________ ______ 
                                  |        |        |        |      |        |        |        |      |                              
                                  |        |        |        |      |        |        |        |      |                
                                  |        |        |        |______|        |        |        |______|
                                  |________|________|________|      |________|________|________|      |                
                                  |        |        |        |      |        |        |        |      |                             
                                  |        |        |        |______|        |        |        |______|                             
                                  |        |        |        |      |        |        |        |      |                              
                                  |________|________|________|      |________|________|________|      |                                                         
                                  |        |        |        |______|        |        |        |______|                               
                                  |        |        |        |      |        |        |        |      |                               
                                  |        |        |        |      |        |        |        |      |                      
                                  |______ _|___ ____|_ ______|______|______ _|___ ____|_ ______|______|                              
                                  |      |     |      |      |      |      |     |      |      |      |
                                  |      |     |      |      |      |      |     |      |      |      |                             
                                  |______|_ ___|____ _|______|______|______|_ ___|____ _|______|______|  
                                  |        |        |        |      |        |        |        |      |
                                  |        |        |        |      |        |        |        |      | 
                                  |        |        |        |______|        |        |        |______|                              
                                  |________|________|________|      |________|________|________|      |                               
                                  |        |        |        |      |        |        |        |      |                       
                                  |        |        |        |______|        |        |        |______|                        
                                  |        |        |        |      |        |        |        |      |                        
                                  |________|________|________|      |________|________|________|      |                              
                                  |        |        |        |______|        |        |        |______|                       
                                  |        |        |        |      |        |        |        |      |                         
                                  |        |        |        |      |        |        |        |      |                       
                                  |______ _|___ ____|_ ______|______|______ _|___ ____|_ ______|______|                               
                                  |      |     |      |      |      |      |     |      |      |      |
                                  |      |     |      |      |      |      |     |      |      |      |                        
                                  |______|_ ___|____ _|______|______|______|_ ___|____ _|______|______|  
                                           
                                  
                                                         Square 30 X 30, type 2
                                                          a=3, b=4, s=30, z=36
                                          Equals 4 copies of primitive square 15 X 15 with z=9 


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





                                   ________________ _________________ _________________ ____________
                                  |                |                 |                 |            |
                                  |                |                 |                 |            |
                                  |                |                 |                 |            |
                                  |                |                 |                 |            |
                                  |                |                 |                 |            |
                                  |                |                 |                 |____________|
                                  |                |                 |                 |            |
                                  |________________|_________________|_________________|            |
                                  |                |                 |                 |            |
                                  |                |                 |                 |            |
                                  |                |                 |                 |            |
                                  |                |                 |                 |____________|
                                  |                |                 |                 |            |
                                  |                |                 |                 |            |
                                  |                |                 |                 |            |
                                  |________________|_________________|_________________|            |
                                  |                |                 |                 |            |
                                  |                |                 |                 |____________|
                                  |                |                 |                 |            |
                                  |                |                 |                 |            |
                                  |                |                 |                 |            |
                                  |                |                 |                 |            |
                                  |                |                 |                 |            |
                                  |____________ ___|_________ _______|____ ____________|____________|                    
                                  |            |             |            |            |            |
                                  |            |             |            |            |            |
                                  |            |             |            |            |            |
                                  |            |             |            |            |            |
                                  |            |             |            |            |            |
                                  |____________|_____________|____________|____________|____________| 

                                                         Square 30 X 30, type 2
                                                           a=6, b=8, s=30, z=9
                                                     Elementary square 30 X 30 with z=9