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

1,4

Comments

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

Links

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

Example

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 ...
...

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.

Sequence in context: A016095 A298309 A349205 * A349207 A253581 A165464

Adjacent sequences: A181396 A181397 A181398 * A181400 A181401 A181402

Keyword

nonn,tabl

Author

David Scambler, Oct 17 2010

Extensions

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

Status

approved