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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.

%I A217631 #12 Jul 22 2025 23:41:10
%S A217631 0,2,6,16,38,98,244,614,1542,3872,9726,24426,61348,154078,386974,
%T A217631 971904,2440982,6130642,15397396,38671286,97124758,243933408,
%U A217631 612650254,1538699994,3864517572,9705918062,24376870766,61223660096,153766108518
%N 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.
%C A217631 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
%C A217631 Column 2 of A217637.
%H A217631 R. H. Hardin, <a href="/A217631/b217631.txt">Table of n, a(n) for n = 0..210</a>
%H A217631 R. Euler, P. Oleksik, Z. Skupien, <a href="http://dx.doi.org/10.7151/dmgt.1707">Counting Maximal Distance-Independent Sets in Grid Graphs</a>, 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
%F A217631 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
%F A217631 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)
%e A217631 Some solutions for n=3
%e A217631 ..0..0....0..0....0..0....1..1....0..0....1..0....1..0....0..1....1..1....0..0
%e A217631 ..0..1....0..0....0..1....0..1....1..0....0..0....0..0....0..0....1..1....1..0
%e A217631 ..0..0....1..0....1..1....0..0....0..0....0..0....1..0....0..1....1..1....1..1
%Y A217631 Cf. A217632, A217637.
%K A217631 nonn
%O A217631 0,2
%A A217631 _R. H. Hardin_ Oct 09 2012