%I #7 Nov 30 2018 10:05:15

%S 470,1142,2402,4790,12302,27242,55766,148022,332738,688646,1847582,

%T 4175018,8671142,23345702,52842914,109873622,296146862,670682474,

%U 1395012278,3761354582,8519745410,17722964198,47791500542,108256965290

%N Number of (n+2) X (1+2) 0..3 arrays with every 3 X 3 subblock row and column sum 3 or 6 and every diagonal and antidiagonal sum not 3 or 6.

%H R. H. Hardin, <a href="/A251772/b251772.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 16*a(n-3) - 16*a(n-4) - 39*a(n-6) + 39*a(n-7) - 36*a(n-9) + 36*a(n-10).

%F Empirical g.f.: 2*x*(235 + 336*x + 630*x^2 - 2566*x^3 - 1620*x^4 - 2610*x^5 + 4323*x^6 - 864*x^7 - 2592*x^8 + 4788*x^9) / ((1 - x)*(1 - 4*x^3)*(1 - 12*x^3 - 9*x^6)). - _Colin Barker_, Nov 30 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Column 1 of A251779.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 08 2014