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A185406 1/7 the number of nX3 0..6 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

%I A185406 #9 Jul 22 2025 09:45:25
%S A185406 1,150,5040,279918,12205368,595974240,27536905674,1306753756812,
%T A185406 61210525548816,2885367241303254,135594323017300224,
%U A185406 6381618680273394960,300126625465471449282,14119903429577075460420,664177642891735878467280
%N A185406 1/7 the number of nX3 0..6 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.
%C A185406 Column 3 of A185409
%H A185406 R. H. Hardin, <a href="/A185406/b185406.txt">Table of n, a(n) for n = 1..200</a>
%F A185406 Empirical: a(n)=27*a(n-1)+1101*a(n-2)-5388*a(n-3)-99699*a(n-4)+111696*a(n-5)+1303703*a(n-6)+1272279*a(n-7)-3839565*a(n-8)-46276758*a(n-9)+164100009*a(n-10)-201107172*a(n-11)-398097784*a(n-12)-1098237564*a(n-13)+6484304364*a(n-14)+1678354992*a(n-15)-32033066112*a(n-16)+111598281360*a(n-17)+135161638848*a(n-18)-357171462144*a(n-19)-773247897216*a(n-20)-848592391680*a(n-21)-825363302400*a(n-22)-1632586752000*a(n-23)
%e A185406 Some solutions for 5X3 with a(1,1)=0
%e A185406 ..0..0..3....0..0..3....0..0..4....0..0..3....0..0..4....0..0..3....0..0..0
%e A185406 ..0..2..3....0..0..3....0..0..4....0..1..3....0..0..4....0..0..3....0..1..0
%e A185406 ..0..2..3....6..6..6....2..1..1....6..1..0....1..1..0....2..3..3....6..1..3
%e A185406 ..5..2..4....4..4..2....2..1..3....6..3..0....2..1..0....2..0..6....6..6..3
%e A185406 ..5..4..4....0..0..2....0..0..3....6..3..3....2..2..0....2..0..6....1..1..3
%K A185406 nonn
%O A185406 1,2
%A A185406 _R. H. Hardin_ Jan 26 2011