A204281 - OEIS

A204281

Number of (n+2) X 7 0..2 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..2 introduced in row major order.

%I #8 Jun 06 2018 15:40:03

%S 5263,539,334,442,736,996,2168,5368,13024,34864,94528,255360,696608,

%T 1902112,5191264,14181088,38741728,105833952,289140704,789944032,

%U 2158146784,5896160992,16108605664,44009488608,120236147936,328491253984

%N Number of (n+2) X 7 0..2 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..2 introduced in row major order.

%C Column 5 of A204284.

%H R. H. Hardin, <a href="/A204281/b204281.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) -6*a(n-4) +4*a(n-6) for n>8.

%F Empirical g.f.: x*(5263 - 15250*x - 1283*x^2 - 560*x^3 + 30988*x^4 + 2022*x^5 - 19868*x^6 - 640*x^7) / ((1 - x)*(1 - 2*x - 2*x^2)*(1 - 2*x^3)). - _Colin Barker_, Jun 06 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Cf. A204284.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 13 2012