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Number of n X 4 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 #8 May 09 2018 11:10:19

%S 1,7,39,145,797,3569,17175,81389,385231,1829101,8668831,41113007,

%T 194955001,924449179,4383753391,20787435021,98573175383,467429309303,

%U 2216527199343,10510668481659,49841089379745,236344089239897

%N Number of n X 4 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 4 of A196786.

%H R. H. Hardin, <a href="/A196782/b196782.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +10*a(n-2) +15*a(n-3) -a(n-4) -6*a(n-5) -28*a(n-6) -14*a(n-7) +13*a(n-8) -13*a(n-9) +3*a(n-10).

%F Empirical g.f.: x*(1 + 5*x + 15*x^2 - 18*x^3 + 13*x^4 - 47*x^5 + x^6 - 17*x^7 + 12*x^8 + 3*x^9) / (1 - 2*x - 10*x^2 - 15*x^3 + x^4 + 6*x^5 + 28*x^6 + 14*x^7 - 13*x^8 + 13*x^9 - 3*x^10). - _Colin Barker_, May 09 2018

%e Some solutions for n=5:

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

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

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

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

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

%Y Cf. A196786.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 06 2011