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A183365 Number of nX3 binary arrays with no element equal to the sum mod 3 of its horizontal and vertical neighbors.

%I A183365 #7 Jul 22 2025 08:52:10
%S A183365 2,5,18,39,108,288,795,2278,6438,18394,52556,150565,431730,1238954,
%T A183365 3556322,10210036,29317763,84190569,241782416,694380738,1994246166,
%U A183365 5727497628,16449560195,47243891395,135686993036,389700996218
%N A183365 Number of nX3 binary arrays with no element equal to the sum mod 3 of its horizontal and vertical neighbors.
%C A183365 Column 3 of A183368
%H A183365 R. H. Hardin, <a href="/A183365/b183365.txt">Table of n, a(n) for n = 1..200</a>
%F A183365 Empirical: a(n)=3*a(n-1)+a(n-3)-4*a(n-4)+4*a(n-5)-22*a(n-6)-12*a(n-7)-21*a(n-8)+22*a(n-9)-13*a(n-10)+115*a(n-11)+79*a(n-12)+116*a(n-13)-45*a(n-14)+172*a(n-15)-75*a(n-16)-54*a(n-17)-181*a(n-18)-85*a(n-19)-61*a(n-20)-11*a(n-21)-158*a(n-22)+80*a(n-23)+157*a(n-24)+215*a(n-25)-78*a(n-26)-211*a(n-27)-196*a(n-28)-51*a(n-29)+44*a(n-30)+81*a(n-31)+64*a(n-32)+13*a(n-33)-13*a(n-34)-12*a(n-35)-7*a(n-36)-a(n-37)+a(n-38)+a(n-39)
%e A183365 Some solutions for 5X3
%e A183365 ..1..0..1....1..1..1....0..1..1....0..0..0....1..1..0....0..1..1....1..1..0
%e A183365 ..0..0..0....1..1..1....1..1..1....1..1..1....1..1..0....0..1..1....1..1..0
%e A183365 ..1..1..0....0..0..0....1..0..1....1..1..1....1..1..0....0..1..1....0..0..1
%e A183365 ..1..1..0....0..0..1....1..1..1....0..0..0....0..1..1....0..1..1....1..0..0
%e A183365 ..0..0..1....1..0..0....1..1..0....0..1..0....0..1..1....1..0..0....0..1..0
%K A183365 nonn
%O A183365 1,1
%A A183365 _R. H. Hardin_ Jan 04 2011