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Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,4,3,0,1 for x=0,1,2,3,4
1

%I #5 Mar 31 2012 12:36:27

%S 1,17,135,797,6137,40749,289761,2025511,14215709,99646153,698024127,

%T 4892934573,34291191221,240334383531,1684405081345,11805196899669,

%U 82737396174443,579869401345235,4064046980256775,28483094044958233

%N Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,4,3,0,1 for x=0,1,2,3,4

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

%C Column 5 of A196786

%H R. H. Hardin, <a href="/A196783/b196783.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +18*a(n-2) +75*a(n-3) +214*a(n-4) +573*a(n-5) +1067*a(n-6) +496*a(n-7) -6999*a(n-8) -22187*a(n-9) -27738*a(n-10) -36490*a(n-11) +38397*a(n-12) +191499*a(n-13) +139688*a(n-14) +174635*a(n-15) +145499*a(n-16) -220926*a(n-17) -251717*a(n-18) -362124*a(n-19) -163792*a(n-20) +83311*a(n-21) -300598*a(n-22) +162970*a(n-23) -92220*a(n-24) +10134*a(n-25) -10370*a(n-26) -8340*a(n-27) +8044*a(n-28) -432*a(n-29) +448*a(n-30) -128*a(n-31)

%e Some solutions for n=4

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

%e ..0..0..0..3..0....1..4..1..0..0....3..0..0..0..3....0..0..3..0..0

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_ Oct 06 2011