The investigation of coin combinations

Combination for 10p: 10p

For 20p:10+10, 20

For 30p: 10+10+10, 20+10, 10+20

For 40p: 10+10+10+10+10, 20+10+10, 10+20+10, 10+10+20, 20+20

And so on. I got this table of results.  

As you can see there is no pattern that is because these results follow the Fabernacci sequence where the previous 2 values e.g 5+8 added together equal the next  value, 13. With this in mind you can predict that the next value will be 55+89=144

To see if other values of coins did this I tried it with 10p and 30p’s.

This doesn’t follow the Fibernacci sequence in the early values only in the later ones like70, 80 and 90p

I used other values of coins and came up with this graph. 

This is the graph I came up with as you can see It doesn’t follow a set pattern, only the 10p 20p combinations follow the Fibernacci sequence the rest seem to be irregular. I did not manage to find an nth term for any of the coin combinations but you can use the graph to find out values. That proves that there is a linear equation the equals the corresponding line on the graph but I have been unable to find it.