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%I #5 Mar 31 2012 12:36:27
%S 3,37,298,2425,19580,156862,1272373,10339597,83584679,675742932,
%T 5470806427,44295902902,358490386914,2901075834539,23480627788151,
%U 190053072058627,1538212852796494,12449506279663245,100761743839068352
%N Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,2,1,0,4 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 0's, every 4 is next to 4 4's
%C Column 4 of A196982
%H R. H. Hardin, <a href="/A196978/b196978.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n-1) +16*a(n-2) +150*a(n-3) +815*a(n-4) +1826*a(n-5) -1572*a(n-6) -21876*a(n-7) -31637*a(n-8) +20026*a(n-9) +32784*a(n-10) -91598*a(n-11) -422974*a(n-12) +432740*a(n-13) +3523616*a(n-14) +3600194*a(n-15) +234087*a(n-16) -11219026*a(n-17) -7109671*a(n-18) +19311932*a(n-19) -9277085*a(n-20) -24160816*a(n-21) -110533811*a(n-22) -3516954*a(n-23) +241335579*a(n-24) +160959342*a(n-25) +42003302*a(n-26) -265144751*a(n-27) -505651035*a(n-28) -98733204*a(n-29) +460759858*a(n-30) +551357778*a(n-31) +98951371*a(n-32) -538468841*a(n-33) -445294645*a(n-34) +238119056*a(n-35) +265509889*a(n-36) -21010621*a(n-37) +7105528*a(n-38) -10150162*a(n-39) -68879020*a(n-40) -3789904*a(n-41) +26738204*a(n-42) -1322843*a(n-43) +299876*a(n-44) +2030016*a(n-45) -2426011*a(n-46) -310065*a(n-47) +372546*a(n-48) -2994*a(n-49) +41431*a(n-50) +3045*a(n-51) -10905*a(n-52) -1956*a(n-53) +342*a(n-54) +51*a(n-55) +90*a(n-56) +27*a(n-57) -9*a(n-58)
%e Some solutions for n=5
%e ..1..2..1..0....1..1..2..1....0..1..2..1....0..0..1..0....1..2..1..0
%e ..1..0..1..2....2..0..0..0....0..1..2..1....0..0..2..1....1..2..0..0
%e ..2..0..0..1....1..1..2..0....0..0..0..0....0..1..0..0....1..1..0..0
%e ..1..0..0..0....0..0..1..1....0..1..1..0....0..2..2..1....2..1..1..0
%e ..1..2..1..0....0..0..1..2....1..2..2..1....0..1..1..0....0..0..2..1
%K nonn
%O 1,1
%A _R. H. Hardin_ Oct 08 2011
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