A181399 Summed lengths of nonintersecting rook paths on an n X k board (square array by antidiagonals).

0, 1, 1, 2, 4, 2, 3, 14, 14, 3, 4, 40, 64, 40, 4, 5, 104, 284, 284, 104, 5, 6, 256, 1206, 1912, 1206, 256, 6, 7, 608, 4882, 13132, 13132, 4882, 608, 7, 8, 1408, 19060, 88608, 148432, 88608, 19060, 1408, 8, 9, 3200, 72588, 577727, 1692480, 1692480, 577727, 72588, 3200, 9

Offset: 1

Author

David Scambler, Oct 17 2010

Keywords

• nonn
• tabl

Comments

Paths are self-avoiding from one corner to the diagonally opposite corner.

Examples

			Array starts:
======================================================
n\k| 1   2     3      4        5        6        7
---|--------------------------------------------------
1  | 0   1     2      3        4        5        6 ...
2  | 1   4    14     40      104      256      608 ...
3  | 2  14    64    284     1206     4882    19060 ...
4  | 3  40   284   1912    13132    88608   577727 ...
5  | 4 104  1206  13132   148432  1692480 18893254 ...
6  | 5 256  4882  88608  1692480 32871240 ...
7  | 6 608 19060 577727 18893254 ...
...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..378 (terms 1..66 from David Scambler)

Crossrefs

Related sequences: A181394 (3 X n), A181395 (4 X n), A181396 (5 X n), A181397 (6 X n), A181398 (n X n).

The number of these paths is given in A064298.

Extensions

a(55) and a(60) in b-file corrected by Andrew Howroyd, Feb 23 2018