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Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,1,0,3 for x=0,1,2,3,4
1

%I #5 Mar 31 2012 12:36:28

%S 2,16,100,588,3649,22210,135560,827698,5055418,30875671,188551113,

%T 1151456304,7031841993,42943005672,262250032226,1601541435978,

%U 9780493464535,59728749093644,364759066990417,2227556706954487

%N Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,1,0,3 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 0's, every 4 is next to 4 3's

%C Column 3 of A197207

%H R. H. Hardin, <a href="/A197202/b197202.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 3*a(n-1) +6*a(n-2) +53*a(n-3) +91*a(n-4) +341*a(n-5) +491*a(n-6) +357*a(n-7) -1335*a(n-8) -2465*a(n-9) -5726*a(n-10) -7838*a(n-11) -6330*a(n-12) +5436*a(n-13) +31522*a(n-14) +34477*a(n-15) +22496*a(n-16) -22333*a(n-17) -35514*a(n-18) -40845*a(n-19) -2186*a(n-20) -2851*a(n-21) -4657*a(n-22) +24365*a(n-23) +3052*a(n-24) +5609*a(n-25) -758*a(n-26) -165*a(n-27) +820*a(n-28) +665*a(n-29) +55*a(n-30) +81*a(n-31) +28*a(n-32)

%e Some solutions for n=4

%e ..1..0..1....1..0..0....0..2..1....0..3..0....0..3..0....1..1..0....0..1..1

%e ..2..0..2....2..3..0....1..1..0....1..0..0....0..0..3....2..2..1....1..2..2

%e ..1..0..1....1..0..3....2..0..3....2..1..1....1..2..0....1..0..1....0..0..1

%e ..0..0..0....0..3..0....1..0..0....0..1..2....0..1..0....0..1..2....1..2..1

%K nonn

%O 1,1

%A _R. H. Hardin_ Oct 11 2011