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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 1,4,0,2,3 for x=0,1,2,3,4
1

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

%S 3,23,88,495,2223,10854,53647,262013,1280764,6254945,30578633,

%T 149503874,730808203,3572316883,17462371522,85361430021,417272087661,

%U 2039743998384,9970847387767,48740355602949,238256829183690,1164667576556219

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

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

%C Column 4 of A196343

%H R. H. Hardin, <a href="/A196339/b196339.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) +56*a(n-4) +84*a(n-5) -35*a(n-6) -304*a(n-7) -675*a(n-8) -1177*a(n-9) -936*a(n-10) +247*a(n-11) +1040*a(n-12) +616*a(n-13) -301*a(n-14) -617*a(n-15) -204*a(n-16) +999*a(n-17) +2210*a(n-18) +1973*a(n-19) +68*a(n-20) -1440*a(n-21) -1074*a(n-22) -47*a(n-23) +267*a(n-24) +42*a(n-25) -22*a(n-26) +35*a(n-27) +17*a(n-28) -14*a(n-29) -3*a(n-30) +2*a(n-31)

%e Some solutions for n=5

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Oct 01 2011