A252694 - OEIS

A252694

Number of (n+2) X (7+2) 0..3 arrays with every consecutive three elements in every row and column having exactly two distinct values, and in every diagonal and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order.

%I #7 Dec 05 2018 08:11:12

%S 3703,6483,727,12740,1276,25382,2592,51060,5944,103716,15052,213524,

%T 41692,449132,125580,979212,407404,2261532,1405516,5679404,5082844,

%U 15835820,19012140,49190076,72778060,167430252,282915484,608379116

%N Number of (n+2) X (7+2) 0..3 arrays with every consecutive three elements in every row and column having exactly two distinct values, and in every diagonal and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order.

%H R. H. Hardin, <a href="/A252694/b252694.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 7*a(n-3) + 2*a(n-4) + 6*a(n-5) + 14*a(n-6) - 20*a(n-7) - 4*a(n-8) + 8*a(n-9) for n>10.

%F Empirical g.f.: x*(3703 - 8329*x - 17799*x^2 + 48719*x^3 - 10255*x^4 + 15663*x^5 - 99398*x^6 + 53844*x^7 + 39864*x^8 - 25728*x^9) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 2*x^3)). - _Colin Barker_, Dec 05 2018

%e Some solutions for n=4:

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

%e ..2..3..2..3..2..3..2..3..2....2..3..2..3..2..3..2..3..2

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

%e ..2..3..2..3..2..2..3..2..2....3..2..3..2..3..2..3..2..3

%Y Column 7 of A252695.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 20 2014