A252945 - OEIS

%I #9 Dec 07 2018 11:52:03

%S 198,747,2970,11943,48024,193059,776160,3120579,12546540,50444415,

%T 202816008,815438907,3278541276,13181653431,52997956416,213082782147,

%U 856717412004,3444505073199,13848925017096,55680778531323

%N Number of (n+2) X (1+2) 0..2 arrays with every consecutive three elements in every row, column and nw-se diagonal having exactly two distinct values, and new values 0 upwards introduced in row major order.

%H R. H. Hardin, <a href="/A252945/b252945.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: 9*x*(22 - 49*x + 30*x^2 + 6*x^3 - 32*x^4 + 24*x^5) / ((1 - x)*(1 - 5*x + 4*x^2 - 2*x^4 + 4*x^5)). - _Colin Barker_, Dec 07 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Column 1 of A252952.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 25 2014