A068416 Number of partitionings of n X n checkerboard into two edgewise-connected sets.
0, 6, 53, 627, 16213, 1123743, 221984391, 127561384993, 215767063451331, 1082828220389781579, 16209089366362071416785, 726438398002211876667379681, 97741115155002465272674416929195, 39565596445488219947994403962984729307
Offset: 1
Keywords
Examples
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
Links
- Anthony J. Guttmann and Iwan Jensen, Table of n, a(n) for n = 1..26
- Benjamin Fifield, Kosuke Imai, Jun Kawahara, and 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.
- Eric Weisstein's World of Mathematics, Grid Graph.
- Eric Weisstein's World of Mathematics, Minimal Edge Cut.
Formula
a(n) = A166755(n)/2. - Andrew Howroyd, Dec 11 2024
Extensions
a(7)-a(14) from Andrew Howroyd, Apr 14 2016
Comments