On a 10x10 "chessboard" a token is placed on the leftmost square of the bottom line a.k.a. a1.
You can move said token either one step to the right or one step up within the same column or one step diagonally
(combining right and up).
To make it clear from c4 you may advance in one step to c5, c6 or d6.
How many distinct routes exist to reach the top line's rightmost square (i.e. j10?
(In reply to Another way to avoid tedium.
The formula presented as C(n,r) of course is not the combination function that we usually represent as C(n,r), but the arbitrary function that fits this problem. The OEIS uses m(i,j).
But I think that your method of avoiding the tedium is to use the numbers found early in the sequence to look up the sequence in OEIS, rather than using the formula all the way through to (10,10), if I'm reading it correctly.
Posted by Charlie
on 2014-12-07 10:32:56