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A068416
Number of partitionings of n X n checkerboard into two edgewise-connected sets.
3
0, 6, 53, 627, 16213, 1123743, 221984391, 127561384993, 215767063451331, 1082828220389781579, 16209089366362071416785, 726438398002211876667379681, 97741115155002465272674416929195, 39565596445488219947994403962984729307
OFFSET
1,2
COMMENTS
One of the partitions may completely surround the other. (Cf. A271802) - Andrew Howroyd, Apr 14 2016
LINKS
Anthony J. Guttmann and Iwan Jensen, Table of n, a(n) for n = 1..26
Benjamin Fifield, Kosuke Imai, Jun Kawahara, Christopher T. Kenny, The Essential Role of Empirical Validation in Legislative Redistricting Simulation, Tech. rep., Department of Government and Department of Statistics, Harvard University (2019).
Anthony J. Guttmann and Iwan Jensen, The gerrymander sequence, or A348456, arXiv:2211.14482 [math.CO], 2022.
FORMULA
a(n) = A271802(n) + A140517(n-2). - Andrew Howroyd, Apr 14 2016
EXAMPLE
Illustration of a(2)=6:
11 12 12 12 11 11
22 12 22 11 12 21
Illustration of a few solutions of a(3):
111 112 122 111 111
121 111 112 212 111
111 111 222 222 222
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 02 2002
EXTENSIONS
a(7)-a(14) from Andrew Howroyd, Apr 14 2016
STATUS
approved