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

%I #5 Mar 31 2012 12:36:26

%S 3,23,76,391,1895,8118,37661,172339,791490,3631677,16619517,76129750,

%T 348810191,1598275415,7323187236,33551912535,153722248869,

%U 704306601498,3226924900161,14784806391213,67739415602004,310360945033631

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

%C Every 0 is next to 0 3'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 1's

%C Column 4 of A196653

%H R. H. Hardin, <a href="/A196649/b196649.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) +4*a(n-2) +15*a(n-3) +49*a(n-4) +153*a(n-5) +219*a(n-6) +248*a(n-7) +189*a(n-8) -221*a(n-9) -683*a(n-10) -1258*a(n-11) -1587*a(n-12) -1789*a(n-13) -1966*a(n-14) -1966*a(n-15) -2193*a(n-16) -2166*a(n-17) -1860*a(n-18) -1625*a(n-19) -1338*a(n-20) -926*a(n-21) -354*a(n-22) +109*a(n-23) +327*a(n-24) +485*a(n-25) +372*a(n-26) +164*a(n-27) +17*a(n-28) +11*a(n-29) +21*a(n-30) -7*a(n-31) -12*a(n-32) -3*a(n-33) +2*a(n-34)

%e Some solutions for n=5

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

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

%e ..0..0..0..2....1..4..1..0....0..1..4..1....0..0..2..2....1..4..1..0

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Oct 04 2011