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A197212 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,3,2,1,0 for x=0,1,2,3,4. 1

%I

%S 1,5,14,44,149,479,1537,4971,16088,52020,168111,543379,1756623,

%T 5678611,18356490,59338576,191817551,620069245,2004431603,6479507953,

%U 20945607368,67708621756,218874399841,707531760601,2287161925185,7393462782885

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

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

%C Column 3 of A197217.

%H R. H. Hardin, <a href="/A197212/b197212.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) +8*a(n-3) +10*a(n-4) +16*a(n-5) +8*a(n-6) +6*a(n-7) -8*a(n-8) -12*a(n-9) -10*a(n-10) -4*a(n-11) -a(n-12).

%F Empirical g.f.: x*(1 + 3*x + 4*x^2 + 8*x^3 + 11*x^4 + 3*x^5 - x^6 - 5*x^7 - 14*x^8 - 10*x^9 - 5*x^10 - x^11) / (1 - 2*x - 8*x^3 - 10*x^4 - 16*x^5 - 8*x^6 - 6*x^7 + 8*x^8 + 12*x^9 + 10*x^10 + 4*x^11 + x^12). - _Colin Barker_, May 11 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A197217.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 11 2011

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Last modified January 25 08:59 EST 2021. Contains 340416 sequences. (Running on oeis4.)