Programming puzzle question. Can anyone out there help me?
You are given a set of blocks to build a panel using 3”×1” and 4.5”×1" blocks. 

For structural integrity, the spaces between the blocks must not line up in adjacent rows. 

There are 2 ways in which to build a 7.5”×1” panel, 2 ways to build a 7.5”×2” panel, 4 ways to build a 12”×3” panel, and 7958 ways to build a 27”×5” panel. How many different ways are there to build a 48”×10” panel? 


This is what I understand so far:

with the blocks **3 x 1** and **4.5 x 1**



I've used combination formula to find all possible combinations that the 2 blocks can be arranged in a panel of this size

**C = choose --> C(n, k) = n!/r!(n-r)! combination of group n at r at a time**

**Panel: 7.5 x 1 = 2 ways** -->
                          
1 (3 x 1 block) and 1 (4.5 x 1 block) --> Only 2 blocks are used--> 2 C 1 = **2 ways**


**Panel: 7.5 x 2 = 2 ways**

I used combination here as well
                           
1(3 x 1 block) and 1 (4.5 x 1 block) --> 2 C 1 = **2 ways**


**Panel: 12 x 3 panel = 2 ways** -->

                           
2(4.5 x 1 block) and 1(3 x 1 block) --> 3 C 1 = **3 ways**

0(4.5 x 1 block) and 4(3 x 1 block) --> 4 C 0 = **1 way**

3 ways + 1 way = **4 ways**

**(This is where I get confused)**

**Panel 27 x 5 panel = 7958 ways**

6(4.5 x 1 block) and 0(3 x 1) --> 6 C 0 = **1 way**

4(4.5 x 1 block) and 3(3 x 1 block) --> 7 C 3 = **35 ways**

2(4.5 x 1 block) and 6(3 x 1 block) --> 8 C 2 = **28 ways**

0(4.5 x 1 block) and 9(3 x 1 block) --> 9 C 0 = **1 way**

1 way + 35 ways + 28 ways + 1 way = **65 ways**

As you can see here the number of ways is nowhere near 7958. What am I doing wrong here?

Also how would I find how many ways there are to construct a 48 x 10 panel?
Because it's a little difficult to do it by hand especially when trying to find 7958 ways. 

How would write a program to calculate an answer for the number of ways for a 7958 panel?
Would it be easier to construct a program to calculate the result? Any help would be greatly appreciated.






Programming puzzle question. Can anyone out there help me?
===

You are given a set of blocks to build a panel using 3”×1” and 4.5”×1" blocks. 

For structural integrity, the spaces between the blocks must not line up in adjacent rows. 

There are 2 ways in which to build a 7.5”×1” panel, 2 ways to build a 7.5”×2” panel, 4 ways to build a 12”×3” panel, and 7958 ways to build a 27”×5” panel. How many different ways are there to build a 48”×10” panel? 


This is what I understand so far:

with the blocks **3 x 1** and **4.5 x 1**



I've used combination formula to find all possible combinations that the 2 blocks can be arranged in a panel of this size

**C = choose --> C(n, k) = n!/r!(n-r)! combination of group n at r at a time**

**Panel: 7.5 x 1 = 2 ways** -->
                          
1 (3 x 1 block) and 1 (4.5 x 1 block) --> Only 2 blocks are used--> 2 C 1 = **2 ways**


**Panel: 7.5 x 2 = 2 ways**

I used combination here as well
                           
1(3 x 1 block) and 1 (4.5 x 1 block) --> 2 C 1 = **2 ways**


**Panel: 12 x 3 panel = 2 ways** -->

                           
2(4.5 x 1 block) and 1(3 x 1 block) --> 3 C 1 = **3 ways**

0(4.5 x 1 block) and 4(3 x 1 block) --> 4 C 0 = **1 way**

3 ways + 1 way = **4 ways**

**(This is where I get confused)**

**Panel 27 x 5 panel = 7958 ways**

6(4.5 x 1 block) and 0(3 x 1) --> 6 C 0 = **1 way**

4(4.5 x 1 block) and 3(3 x 1 block) --> 7 C 3 = **35 ways**

2(4.5 x 1 block) and 6(3 x 1 block) --> 8 C 2 = **28 ways**

0(4.5 x 1 block) and 9(3 x 1 block) --> 9 C 0 = **1 way**

1 way + 35 ways + 28 ways + 1 way = **65 ways**

As you can see here the number of ways is nowhere near 7958. What am I doing wrong here?

Also how would I find how many ways there are to construct a 48 x 10 panel?
Because it's a little difficult to do it by hand especially when trying to find 7958 ways. 

How would write a program to calculate an answer for the number of ways for a 7958 panel?
Would it be easier to construct a program to calculate the result? Any help would be greatly appreciated.





