A068416 - OEIS

%I #29 Nov 29 2022 01:34:13

%S 0,6,53,627,16213,1123743,221984391,127561384993,215767063451331,

%T 1082828220389781579,16209089366362071416785,

%U 726438398002211876667379681,97741115155002465272674416929195,39565596445488219947994403962984729307

%N Number of partitionings of n X n checkerboard into two edgewise-connected sets.

%C One of the partitions may completely surround the other. (Cf. A271802) - _Andrew Howroyd_, Apr 14 2016

%H Anthony J. Guttmann and Iwan Jensen, <a href="/A068416/b068416.txt">Table of n, a(n) for n = 1..26</a>

%H Benjamin Fifield, Kosuke Imai, Jun Kawahara, Christopher T. Kenny, <a href="https://imai.fas.harvard.edu/research/files/enumerate.pdf">The Essential Role of Empirical Validation in Legislative Redistricting Simulation</a>, Tech. rep., Department of Government and Department of Statistics, Harvard University (2019).

%H Anthony J. Guttmann and Iwan Jensen, <a href="https://arxiv.org/abs/2211.14482">The gerrymander sequence, or A348456</a>, arXiv:2211.14482 [math.CO], 2022.

%F a(n) = A271802(n) + A140517(n-2). - _Andrew Howroyd_, Apr 14 2016

%e Illustration of a(2)=6:

%e    11   12   12   12   11   11

%e    22   12   22   11   12   21

%e Illustration of a few solutions of a(3):

%e    111   112   122   111   111

%e    121   111   112   212   111

%e    111   111   222   222   222

%Y Cf. A068392, A271802, A068381, A068417, A113900, A348456, A358289.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 02 2002

%E a(7)-a(14) from _Andrew Howroyd_, Apr 14 2016