A217631 Number of nX2 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..1 nX2 array

0, 2, 6, 16, 38, 98, 244, 614, 1542, 3872, 9726, 24426, 61348, 154078, 386974, 971904, 2440982, 6130642, 15397396, 38671286, 97124758, 243933408, 612650254, 1538699994, 3864517572, 9705918062, 24376870766, 61223660096, 153766108518

Offset

0,2

Comments

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

Column 2 of A217637.

Links

R. H. Hardin, Table of n, a(n) for n = 0..210

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

G.f. = (2*x+4*x^2+4*x^3)/(1-x-3*x^2-2*x^3). [Euler et al.] - N. J. A. Sloane, Nov 21 2013

Empirical: a(n) = a(n-1) + 3*a(n-2) + 2*a(n-3). (Follows from g.f. - N. J. A. Sloane, Nov 21 2013)

Example

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

Crossrefs

Cf. A217632, A217637.

Sequence in context: A330886 A265758 A265107 * A046209 A285885 A273348

Adjacent sequences: A217628 A217629 A217630 * A217632 A217633 A217634

Keyword

nonn

Author

R. H. Hardin Oct 09 2012

Status

approved