A217637 T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..1 nXk array.

2, 2, 2, 4, 6, 4, 6, 16, 16, 6, 10, 38, 66, 38, 10, 16, 98, 244, 244, 98, 16, 26, 244, 968, 1418, 968, 244, 26, 42, 614, 3726, 8706, 8706, 3726, 614, 42, 68, 1542, 14520, 52120, 83074, 52120, 14520, 1542, 68, 110, 3872, 56352, 315378, 773348, 773348, 315378

Offset: 1

Author

R. H. Hardin, Oct 09 2012

Keywords

• nonn
• tabl

Comments

Number of maximal independent sets in the graph P_2 X P_n X P_k. - Andrew Howroyd, Jun 10 2017

Examples

			Table starts
...2.....2........4..........6...........10..............16................26
...2.....6.......16.........38...........98.............244...............614
...4....16.......66........244..........968............3726.............14520
...6....38......244.......1418.........8706...........52120............315378
..10....98......968.......8706........83074..........773348...........7272142
..16...244.....3726......52120.......773348........11181454.........163361868
..26...614....14520.....315378......7272142.......163361868........3709621842
..42..1542....56352....1900838.....68138974......2378097084.......83923710538
..68..3872...218978...11472148....639248556.....34661572702.....1901055652804
.110..9726...850620...69210290...5994907930....505010822224....43046530809006
.178.24426..3304624..417586442..56226693158...7358779655656...974841850791586
.288.61348.12837742.2519466108.527340415924.107224919634686.22075731493018104
...
Some solutions for n=3 k=4
..1..0..0..1....0..0..0..1....1..0..1..1....1..1..0..0....1..0..0..0
..0..0..0..0....0..0..1..1....0..0..0..1....0..0..1..0....1..1..0..0
..1..0..0..0....0..0..0..1....1..0..1..1....0..0..0..1....1..0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..220
• MacKenzie Carr, Christina M. Mynhardt, Ortrud R. Oellermann, Enumerating the Digitally Convex Sets of Powers of Cycles and Cartesian Products of Paths and Complete Graphs, arXiv:2008.02781 [math.CO], 2020.
• R. Euler, P. Oleksik, Z. Skupien, Counting Maximal Distance-Independent Sets in Grid Graphs, Discussiones Mathematicae Graph Theory. Volume 33, Issue 3, Pages 531-557, ISSN (Print) 2083-5892, July 2013; see also.

Crossrefs

Columns 1-3 are A006355(n+1), A217631, A217632.

Cf. A197054.