A252856 - OEIS

A252856

Number of (n+2) X (3+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.

%I #8 Dec 07 2018 11:50:15

%S 684,738,1197,1962,3582,6795,12762,24552,47367,91440,176940,342711,

%T 663624,1285704,2490993,4826304,9351324,18119295,35108028,68026230,

%U 131809365,255397428,494865270,958865463,1857925458,3599971020

%N Number of (n+2) X (3+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="/A252856/b252856.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: 9*x*(76 - 70*x - 31*x^2 - 48*x^3 - 38*x^4 + 35*x^5 - 86*x^6 + 95*x^7 - 20*x^8 - 2*x^9) / ((1 - x)*(1 + x + x^2)*(1 - 2*x + x^3 - 2*x^4 + x^5)). - _Colin Barker_, Dec 07 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Column 3 of A252861.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 23 2014