A230701 - OEIS

%I #8 Mar 17 2018 05:46:11

%S 2,8,30,102,348,1172,3956,13326,44916,151338,509978,1718408,5790456,

%T 19511640,65747178,221543696,746521190,2515502046,8476319172,

%U 28562083692,96243740012,324306077270,1092792451740,3682309466130,12408031373682

%N Number of (n+3) X (1+3) 0..2 white square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

%C Column 1 of A230708.

%H R. H. Hardin, <a href="/A230701/b230701.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 3*a(n-2) - 6*a(n-3) + a(n-5).

%F Empirical g.f.: 2*x*(1 + x) / ((1 - x)*(1 - 2*x - 5*x^2 + x^3 + x^4)). - _Colin Barker_, Mar 17 2018

%e Some solutions for n=2:

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

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

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

%e ..x..2..x..0....x..0..x..2....x..0..x..2....x..0..x..0....x..2..x..0

%e ..1..x..1..x....2..x..1..x....2..x..1..x....2..x..2..x....1..x..2..x

%Y Cf. A230708.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 28 2013