A233224 - OEIS

A233224

Number of n X 2 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

%I #9 Oct 10 2018 10:49:41

%S 2,14,174,2541,39203,616454,9757236,154782591,2457231917,39019481264,

%T 619661480574,9841023112761,156289684281383,2482114628442074,

%U 39419748363507816,626045687116778451,9942561014884521857

%N Number of n X 2 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

%H R. H. Hardin, <a href="/A233224/b233224.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 21*a(n-1) - 79*a(n-2) - 41*a(n-3) + 72*a(n-4) + 28*a(n-5).

%F Empirical g.f.: x*(2 - 28*x + 38*x^2 + 75*x^3 + 18*x^4) / ((1 - x)*(1 - 5*x - 2*x^2)*(1 - 15*x - 14*x^2)). - _Colin Barker_, Oct 10 2018

%e Some solutions for n=5:

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

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

%e ..2..0....5..1....0..4....2..2....2..2....1..2....2..2....0..0....2..4....2..0

%e ..1..2....1..5....2..0....4..4....2..2....5..5....1..0....2..2....4..4....1..0

%e ..0..0....5..1....1..2....4..5....1..1....4..5....1..1....1..5....5..5....0..1

%Y Column 2 of A233230.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 06 2013