A197337 - OEIS

%I #9 May 12 2018 08:45:51

%S 1,5,11,38,103,297,856,2458,7045,20229,58099,166807,478862,1374798,

%T 3947115,11332271,32534963,93408015,268175294,769933854,2210486645,

%U 6346325657,18220355429,52310797713,150184749648,431181704516

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

%C Every 0 is next to 0 3'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 2's.

%C Column 3 of A197342.

%H R. H. Hardin, <a href="/A197337/b197337.txt">Table of n, a(n) for n = 1..200</a>

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

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

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A197342.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 13 2011