A271802 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..14.

FORMULA

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

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 *)

CROSSREFS

Sequence in context: A144345 A294158 A209306 * A097820 A166889 A164894

Adjacent sequences: A271799 A271800 A271801 * A271803 A271804 A271805

KEYWORD

nonn

AUTHOR

Andrew Howroyd, Apr 14 2016

STATUS

approved