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%I #5 Mar 31 2012 12:36:28
%S 3,37,306,2573,21826,183864,1566649,13348347,113287557,961919858,
%T 8175928275,69488321244,590397703542,5016197696693,42623892116103,
%U 362188045090417,3077507174666026,26149460063126683,222193621588208558
%N Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,2,1,4,0 for x=0,1,2,3,4
%C Every 0 is next to 0 3's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 4's, every 4 is next to 4 0's
%C Column 4 of A197167
%H R. H. Hardin, <a href="/A197163/b197163.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) +17*a(n-2) +149*a(n-3) +813*a(n-4) +1326*a(n-5) -3717*a(n-6) -22329*a(n-7) -16169*a(n-8) +41608*a(n-9) -28103*a(n-10) -147920*a(n-11) +3614*a(n-12) +1500818*a(n-13) +3182258*a(n-14) -2568362*a(n-15) -6073404*a(n-16) -6325762*a(n-17) +21785856*a(n-18) +34561892*a(n-19) -77644296*a(n-20) -74358025*a(n-21) -138894121*a(n-22) +307090271*a(n-23) +386259819*a(n-24) -151269205*a(n-25) -185084867*a(n-26) -683118193*a(n-27) -176964137*a(n-28) +695605563*a(n-29) +782662576*a(n-30) +230529279*a(n-31) -990905773*a(n-32) -923405685*a(n-33) +364477890*a(n-34) +906701888*a(n-35) +37283152*a(n-36) -303811604*a(n-37) -30087481*a(n-38) -106325844*a(n-39) -39257294*a(n-40) +96335104*a(n-41) +54342114*a(n-42) -18372831*a(n-43) -556646*a(n-44) -5849368*a(n-45) -6925430*a(n-46) +1795347*a(n-47) +482024*a(n-48) +844027*a(n-49) +78745*a(n-50) -143829*a(n-51) +5674*a(n-52) -49928*a(n-53) -5559*a(n-54) +10194*a(n-55) +2072*a(n-56) -242*a(n-57) -64*a(n-58) -60*a(n-59) -26*a(n-60) +6*a(n-61)
%e Some solutions for n=5
%e ..0..0..2..1....0..1..2..0....0..2..1..1....1..0..1..0....0..0..1..2
%e ..2..1..1..1....0..0..1..0....1..1..1..2....2..0..2..1....1..2..1..1
%e ..1..0..1..2....0..2..1..0....2..1..0..0....1..0..0..1....0..2..1..0
%e ..0..4..0..0....0..1..0..0....0..0..0..1....0..1..1..2....1..1..0..0
%e ..0..0..0..0....0..1..2..1....0..0..1..2....1..2..0..0....2..1..0..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Oct 10 2011
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