A208375 - OEIS

%I #9 Jul 02 2018 05:45:47

%S 10,100,240,420,640,900,1200,1540,1920,2340,2800,3300,3840,4420,5040,

%T 5700,6400,7140,7920,8740,9600,10500,11440,12420,13440,14500,15600,

%U 16740,17920,19140,20400,21700,23040,24420,25840,27300,28800,30340,31920,33540

%N Number of n X 4 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

%C Column 4 of A208379.

%H R. H. Hardin, <a href="/A208375/b208375.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 20*n^2 + 40*n - 60 for n>1.

%F Conjectures from _Colin Barker_, Jul 02 2018: (Start)

%F G.f.: 10*x*(1 + 7*x - 3*x^2 - x^3) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A208379.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 25 2012