Coin sums
In England the currency is made up of pound, £, and pence, p, and there
are eight coins in general circulation:

1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).
It is possible to make £2 in the following way:

1£1 + 150p + 220p + 15p + 12p + 31p
How many different ways can £2 be made using any number of coins?