A208065 - OEIS

%I #8 Jun 27 2018 06:15:47

%S 10,100,240,576,1008,1764,2688,4096,5760,8100,10800,14400,18480,23716,

%T 29568,36864,44928,54756,65520,78400,92400,108900,126720,147456,

%U 169728,195364,222768,254016,287280,324900,364800,409600,456960,509796,565488

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

%C Column 4 of A208069.

%H R. H. Hardin, <a href="/A208065/b208065.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8) for n>9.

%F Conjectures from _Colin Barker_, Jun 27 2018: (Start)

%F G.f.: 2*x*(5 + 40*x + 10*x^2 - 22*x^3 - 12*x^4 - 12*x^5 + 10*x^6 + 10*x^7 - 5*x^8) / ((1 - x)^5*(1 + x)^3).

%F a(n) = n^2*(n + 8)^2/4 for n>1 and even.

%F a(n) = (n - 1)*(n + 1)*(n + 7)*(n + 9)/4 for n>1 and odd.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A208069.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 23 2012