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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 8
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..220

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.

EXAMPLE

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

CROSSREFS

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

Cf. A197054.

Sequence in context: A152968 A222177 A240433 * A231515 A231544 A086420

Adjacent sequences:  A217634 A217635 A217636 * A217638 A217639 A217640

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Oct 09 2012

STATUS

approved

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Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)