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

Author

R. H. Hardin Oct 09 2012

Keywords

• nonn

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.

Examples

			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
		

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

Crossrefs

Cf. A217637.

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