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A186162 1/4 the number of nX3 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

%I A186162 #7 Jul 22 2025 10:16:57
%S A186162 1,48,702,14364,253341,4762206,87054174,1610684397,29645381115,
%T A186162 546876640548,10078456022415,185816448936792,3425262221153151,
%U A186162 63144918326035629,1164039832228952691,21458721711659114403
%N A186162 1/4 the number of nX3 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.
%C A186162 Column 3 of A186168
%H A186162 R. H. Hardin, <a href="/A186162/b186162.txt">Table of n, a(n) for n = 1..200</a>
%F A186162 Empirical: a(n)=12*a(n-1)+138*a(n-2)-297*a(n-3)-1095*a(n-4)-588*a(n-5)+4871*a(n-6)+10632*a(n-7)-24375*a(n-8)+40893*a(n-9)-59724*a(n-10)-68247*a(n-11)-358891*a(n-12)+1270395*a(n-13)+391440*a(n-14)-2188134*a(n-15)+133083*a(n-16)+1270323*a(n-17)+3453273*a(n-18)+1073817*a(n-19)-5417199*a(n-20)-4448358*a(n-21)-13463172*a(n-22)-12754584*a(n-23)
%e A186162 Some solutions for 4X3 with a(1,1)=0
%e A186162 ..0..0..0....0..1..0....0..0..0....0..2..2....0..2..2....0..3..3....0..0..3
%e A186162 ..0..3..3....0..1..0....2..2..0....0..2..3....0..3..1....0..2..2....0..1..3
%e A186162 ..3..1..1....3..1..3....3..2..2....0..3..3....3..3..1....0..1..3....2..1..1
%e A186162 ..3..2..2....3..1..3....3..3..3....1..1..1....1..1..1....1..1..3....2..0..0
%K A186162 nonn
%O A186162 1,2
%A A186162 _R. H. Hardin_ Feb 13 2011