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

1,2

Comments

One of the partitions may completely surround the other. (Cf. A271802) - Andrew Howroyd, Apr 14 2016

Number of minimal edge cuts in the n X n grid graph. - Andrew Howroyd, Dec 11 2024

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) = A271802(n) + A140517(n-2). - Andrew Howroyd, Apr 14 2016

a(n) = A166755(n)/2. - Andrew Howroyd, Dec 11 2024

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

Crossrefs

Cf. A068392, A166755, A271802, A068381, A068417, A113900, A348456, A358289.

Sequence in context: A185148 A243921 A109092 * A360231 A360175 A221413

Adjacent sequences: A068413 A068414 A068415 * A068417 A068418 A068419

Keyword

nonn

Author

R. H. Hardin, Mar 02 2002

Extensions

a(7)-a(14) from Andrew Howroyd, Apr 14 2016

Status

approved