%I #10 Sep 15 2019 04:07:17

%S 0,6,52,614,16000,1114394,220762028,127074234622,215163221802400,

%T 1080509693050320314,16181730102294154610684,

%U 725449589191165593072311582,97631783799192329642727718567824,39528641527526180063041016094650084850

%N Number of cuttings of an n X n checkerboard along grid lines into two pieces with holes disallowed.

%C Equivalently, the number of partitionings of an n X n checkerboard into two edgewise-connected simply-connected sets. (Cf. A068416).

%C Each part is required to contain at least one cell and cuttings are considered different if they only differ by rotation or reflection.

%F a(n) = A068416(n) - A140517(n-2).

%t A068416 = Cases[Import["https://oeis.org/A068416/b068416.txt", "Table"], {_, _}][[All, 2]];

%t A140517 = Cases[Import["https://oeis.org/A140517/b140517.txt", "Table"], {_, _}][[All, 2]];

%t a[n_] := If[n == 1, 0, A068416[[n]] - A140517[[n - 1]]];

%t Array[a, 14] (* _Jean-François Alcover_, Sep 15 2019 *)

%K nonn

%O 1,2

%A _Andrew Howroyd_, Apr 14 2016