Suppose we can only use 5 kinds of tiles to cover a 1 times n board: (1) 1 times 1 size with red color, (2) 1 times 1 size with blue color, (3) 1 times 2 size with black color, (4) 1 times 2 size with green color, (5) 1 times 2 size with white color. Let W(n) be the number of ways to tile the 1 times n board, n=1,2,….

Alex Baird 2022-07-18 Answered
Suppose we can only use 5 kinds of tiles to cover a 1 × n board:
(1) 1 × 1 size with red color,
(2) 1 × 1 size with blue color,
(3) 1 × 2 size with black color,
(4) 1 × 2 size with green color,
(5) 1 × 2 size with white color.
Let W(n) be the number of ways to tile the 1 × n board, n = 1 , 2 ,
For example, W ( 1 ) = 2, W ( 2 ) = 7.
What is the W(n) equation?
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Answers (1)

salumeqi
Answered 2022-07-19 Author has 15 answers
Step 1
W ( n + 1 ) = 2 × W ( n ) + 3 × W ( n 1 )
Step 2
When W ( 0 ) = 1
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