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%I #5 Mar 31 2012 12:36:30
%S 2,14,67,366,1840,9361,47610,242254,1234052,6286646,32024913,
%T 163120939,830844663,4231926412,21555688607,109796116924,559256572765,
%U 2848618914380,14509668521473,73906186682768,376447321305343
%N Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,1,1,1 for x=0,1,2,3,4
%C Every 0 is next to 0 4's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's
%C Column 3 of A197613
%H R. H. Hardin, <a href="/A197608/b197608.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n-1) +6*a(n-2) +26*a(n-3) +53*a(n-4) +232*a(n-5) +501*a(n-6) +551*a(n-7) -245*a(n-8) -2023*a(n-9) -3810*a(n-10) -8322*a(n-11) -13685*a(n-12) -22140*a(n-13) -25568*a(n-14) -31943*a(n-15) -6603*a(n-16) +38551*a(n-17) +60843*a(n-18) +53444*a(n-19) +38044*a(n-20) +14221*a(n-21) +7417*a(n-22) +70469*a(n-23) +71386*a(n-24) +16860*a(n-25) +14396*a(n-26) +8246*a(n-27) +5868*a(n-28) +2756*a(n-29) +716*a(n-30) +240*a(n-31) +48*a(n-32)
%e Some solutions for n=4
%e ..1..1..0....2..1..0....1..1..2....1..2..0....0..0..1....2..1..0....0..0..0
%e ..2..2..0....1..1..2....2..1..1....3..1..0....0..0..2....1..0..0....0..1..0
%e ..1..1..0....0..0..1....0..0..1....1..1..2....0..0..1....0..1..0....1..2..0
%e ..0..0..0....0..0..0....0..1..2....2..1..1....1..2..1....1..2..0....0..0..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Oct 16 2011
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