Quilt Math - Algorithms for Cornerstones and Sashes

I've always found it annoying to have to figure out the number of cornerstones and sashes in my quilts. I'll forget the (usually very odd) numbers, and have to figure them out again, usually by drawing a picture of my quilt and counting. Argh! I was sure that there had to be simple algorithms that covers this, so I asked my math whiz hubby to figure them out. Here are his results: (Note: I always put cornerstones and sashing around all blocks, even the ones on the outer edges of the quilt.)

For a quilt that has n by m blocks, where n is the # row blocks and m is the # column blocks:

The number of cornerstones = (n+1)(m+1)
The number of sashes required = (n+1)m + (m+1)n

So for my Country Chain and Knot quilt, which has 4 rows and 5 columns of blocks:
n=4 and m=5

The # of cornerstones = (4+1)(5+1) = 5x6 = 30 cornerstones
And the # of sashes = (4+1)5 + (5+1)4 = 5x5 + 6x4 = 25+24 = 49 sashes.

Cool! Thanks, Larry!