I just wasn't square enough.

There is actually a connection between odd numbers and square numbers: Take for example the identity: (x+1)^2 = x^2 + 2x + 1 or: (x+1)^2 - x^2 = 2x + 1 Note that 2x+1 is always an odd number because 2x is always even. So to get to the next square number from another you find you corresponding odd number then add it on: e.g. the next square number from 400, 400=20^2 2(20)+1 = 41 therefore the next square number is 441=21^2 This may be the type of pattern spotted before