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Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,3,0,2,4 for x=0,1,2,3,4
1

%I #5 Mar 31 2012 12:36:25

%S 3,23,88,495,2255,10934,54081,264797,1296124,6337697,31018085,

%T 151848926,743248211,3637769547,17804967270,87147406785,426548340739,

%U 2087759457552,10218622797201,50015488523633,244803024488552,1198199184277771

%N Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,3,0,2,4 for x=0,1,2,3,4

%C Every 0 is next to 0 1's, every 1 is next to 1 3's, every 2 is next to 2 0's, every 3 is next to 3 2's, every 4 is next to 4 4's

%C Column 4 of A196322

%H R. H. Hardin, <a href="/A196318/b196318.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) +7*a(n-2) +21*a(n-3) +58*a(n-4) +88*a(n-5) -39*a(n-6) -376*a(n-7) -889*a(n-8) -1593*a(n-9) -1510*a(n-10) -85*a(n-11) +1368*a(n-12) +1434*a(n-13) +535*a(n-14) -241*a(n-15) -814*a(n-16) +291*a(n-17) +3026*a(n-18) +4011*a(n-19) +1232*a(n-20) -2556*a(n-21) -3202*a(n-22) -1051*a(n-23) +553*a(n-24) +418*a(n-25) +110*a(n-26) +93*a(n-27) +13*a(n-28) -44*a(n-29) -5*a(n-30) +6*a(n-31)

%e Some solutions for n=5

%e ..0..2..2..0....0..0..2..0....0..0..0..0....0..2..0..0....0..2..0..0

%e ..0..0..0..0....2..2..2..0....2..0..0..0....0..2..0..0....0..3..2..0

%e ..2..3..2..0....0..0..0..0....3..2..2..2....0..3..2..0....0..2..2..0

%e ..0..2..3..2....0..2..2..2....2..0..0..0....0..2..3..2....0..0..0..0

%e ..2..0..0..0....0..2..0..0....0..0..0..2....0..0..0..0....0..2..2..0

%K nonn

%O 1,1

%A _R. H. Hardin_ Oct 01 2011