A271802 Number of cuttings of an n X n checkerboard along grid lines into two pieces with holes disallowed.

0, 6, 52, 614, 16000, 1114394, 220762028, 127074234622, 215163221802400, 1080509693050320314, 16181730102294154610684, 725449589191165593072311582, 97631783799192329642727718567824, 39528641527526180063041016094650084850

Offset: 1

Author

Andrew Howroyd, Apr 14 2016

Keywords

• nonn

Comments

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

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

Programs

Mathematica

A068416 = Cases[Import["https://oeis.org/A068416/b068416.txt", "Table"], {, }][[All, 2]];
A140517 = Cases[Import["https://oeis.org/A140517/b140517.txt", "Table"], {, }][[All, 2]];
a[n_] := If[n == 1, 0, A068416[[n]] - A140517[[n - 1]]];
Array[a, 14] (* Jean-François Alcover, Sep 15 2019 *)

Formula

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