A252854 - OEIS

%I #8 Dec 07 2018 11:49:45

%S 117,279,684,1719,4383,11286,29241,76059,198324,517923,1353843,

%T 3541014,9265005,24247215,63465660,166131999,434901591,1138526262,

%U 2980601937,7803157779,20428674372,53482546539,140018449419,366571967094

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

%H R. H. Hardin, <a href="/A252854/b252854.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: 9*x*(13 - 21*x - 9*x^2 + 6*x^3) / ((1 - 3*x + x^2)*(1 - x - x^2)). - _Colin Barker_, Dec 07 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Column 1 of A252861.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 23 2014