[seqfan] non-intersecting rook paths from corner to corner

[David Scambler]

Hi fans,

The OEIS contains enumerations of these paths, 3xn: A006192, 4xn A007787, 5xn A007787 etc.

Rather than count them, I have summed their lengths.

1 X n: 0,1,2,3,4,5,6,7,8,9,10
2 X n: 1,4,14,40,104,256,608,1408,3200,7168,15872,
3 X n: 2,14,64,284,1206,4882,19060,72588,271548,1001964,3656480,
4 X n: 3,40,284,1912,13132,88608,577727,3659416,22719964,
5 X n: 4,104,1206,13132,148432,1692480,18893254,
6 X n: 5,256,4882,88608,1692480,32871240,
n X n: 0,4,64,1912,148432,32871240,

The 2 X n case is 2 * A010354; superseeker does not find a formula for the 3 X n case.

Triangle by anti-diagonals of n X k for n, k >= 2

4,
14,14,
40,64,40,
104,284,284,104,
256,1206,1912,1206,256,
608,4882,13132,13132,4882,608,
1408,19060,88608,148432,88608,19060,1408,
3200,72588,577727,1692480,1692480,577727,72588,3200,


Cheers
dave