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%I #21 Jan 08 2020 17:48:57
%S 0,1,1,2,4,2,3,14,14,3,4,40,64,40,4,5,104,284,284,104,5,6,256,1206,
%T 1912,1206,256,6,7,608,4882,13132,13132,4882,608,7,8,1408,19060,88608,
%U 148432,88608,19060,1408,8,9,3200,72588,577727,1692480,1692480,577727,72588,3200,9
%N Summed lengths of nonintersecting rook paths on an n X k board (square array by antidiagonals).
%C Paths are self-avoiding from one corner to the diagonally opposite corner.
%H Andrew Howroyd, <a href="/A181399/b181399.txt">Table of n, a(n) for n = 1..378</a> (terms 1..66 from David Scambler)
%e Array starts:
%e ======================================================
%e n\k| 1 2 3 4 5 6 7
%e ---|--------------------------------------------------
%e 1 | 0 1 2 3 4 5 6 ...
%e 2 | 1 4 14 40 104 256 608 ...
%e 3 | 2 14 64 284 1206 4882 19060 ...
%e 4 | 3 40 284 1912 13132 88608 577727 ...
%e 5 | 4 104 1206 13132 148432 1692480 18893254 ...
%e 6 | 5 256 4882 88608 1692480 32871240 ...
%e 7 | 6 608 19060 577727 18893254 ...
%e ...
%Y Related sequences: A181394 (3 X n), A181395 (4 X n), A181396 (5 X n), A181397 (6 X n), A181398 (n X n).
%Y The number of these paths is given in A064298.
%K nonn,tabl
%O 1,4
%A _David Scambler_, Oct 17 2010
%E a(55) and a(60) in b-file corrected by _Andrew Howroyd_, Feb 23 2018
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