A208138 - OEIS

%I #8 Jun 28 2018 09:37:39

%S 9,81,324,900,2025,3969,7056,11664,18225,27225,39204,54756,74529,

%T 99225,129600,166464,210681,263169,324900,396900,480249,576081,685584,

%U 810000,950625,1108809,1285956,1483524,1703025,1946025,2214144,2509056,2832489

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

%C Column 4 of A208142.

%H R. H. Hardin, <a href="/A208138/b208138.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (9/4)*n^4 + (9/2)*n^3 + (9/4)*n^2.

%F Conjectures from _Colin Barker_, Jun 28 2018: (Start)

%F G.f.: 9*x*(1 + 4*x + x^2) / (1 - x)^5.

%F a(n) = 9*(n^2*(1+n)^2) / 4.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A208142.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 23 2012