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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.

%I A217632 #12 Jul 22 2025 23:41:17
%S A217632 0,4,16,66,244,968,3726,14520,56352,218978,850620,3304624,12837742,
%T A217632 49872976,193747784,752680930,2924043092,11359448344,44129645550,
%U A217632 171436683864,666004286592,2587320999714,10051331417116,39047827550656
%N 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.
%C A217632 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
%C A217632 Column 3 of A217637.
%H A217632 R. H. Hardin, <a href="/A217632/b217632.txt">Table of n, a(n) for n = 0..184</a>
%H A217632 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 A217632 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)
%F A217632 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
%e A217632 Some solutions for n=3
%e A217632 ..1..0..0....0..0..0....0..0..0....1..0..0....0..0..1....0..0..1....1..1..0
%e A217632 ..0..1..0....0..0..0....0..0..1....0..0..0....0..0..1....0..0..1....1..0..0
%e A217632 ..0..0..1....0..1..1....0..0..1....1..0..1....0..0..0....0..0..1....0..0..0
%Y A217632 Cf. A217637.
%K A217632 nonn
%O A217632 0,2
%A A217632 _R. H. Hardin_ Oct 09 2012