A253030 - OEIS

A253030

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

%I #8 Dec 08 2018 11:22:33

%S 1647,12987,102060,802899,6320511,49756086,391717269,3084008175,

%T 24280718976,191165802975,1505081513979,11849778354006,93295489901625,

%U 734532751313235,5783113524612744,45531534681929547,358478297068844223

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

%H R. H. Hardin, <a href="/A253030/b253030.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) - 5*a(n-2) - 10*a(n-3) - 174*a(n-4) + 80*a(n-5) + 160*a(n-6).

%F Empirical g.f.: 27*x*(61 - 68*x - 244*x^2 - 1268*x^3 + 784*x^4 + 1280*x^5) / (1 - 9*x + 5*x^2 + 10*x^3 + 174*x^4 - 80*x^5 - 160*x^6). - _Colin Barker_, Dec 08 2018

%e Some solutions for n=3:

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

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

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

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

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

%Y Column 2 of A253035.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 26 2014