A217632 Number of nX3 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..1 nX3 array

0, 4, 16, 66, 244, 968, 3726, 14520, 56352, 218978, 850620, 3304624, 12837742, 49872976, 193747784, 752680930, 2924043092, 11359448344, 44129645550, 171436683864, 666004286592, 2587320999714, 10051331417116, 39047827550656

Offset

0,2

Comments

Also, number of maximal independent sets in the 3-dimensional (2, 3, n) grid graph. [Euler et al.] - N. J. A. Sloane, Nov 21 2013

Column 3 of A217637.

Links

R. H. Hardin, Table of n, a(n) for n = 0..184

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; http://www.degruyter.com/view/j/dmgt.2013.33.issue-3/dmgt.1707/dmgt.1707.xml

Formula

Empirical: a(n) = 2*a(n-1) +9*a(n-2) -2*a(n-3) -17*a(n-4) -4*a(n-5) +8*a(n-6) -3*a(n-7) +a(n-8) -3*a(n-9) -2*a(n-10) +4*a(n-11)

Euler et al. give an explicit g.f. and recurrence, and so (presumably) prove this recurrence is correct. - N. J. A. Sloane, Nov 21 2013

Example

Some solutions for n=3
..1..0..0....0..0..0....0..0..0....1..0..0....0..0..1....0..0..1....1..1..0
..0..1..0....0..0..0....0..0..1....0..0..0....0..0..1....0..0..1....1..0..0
..0..0..1....0..1..1....0..0..1....1..0..1....0..0..0....0..0..1....0..0..0

Crossrefs

Cf. A217637.

Sequence in context: A026872 A081915 A307878 * A026762 A277871 A082307

Adjacent sequences: A217629 A217630 A217631 * A217633 A217634 A217635

Keyword

nonn

Author

R. H. Hardin Oct 09 2012

Status

approved