A207598 - OEIS

%I #8 Jun 25 2018 06:08:21

%S 40,1600,9240,30400,75400,157440,292600,499840,801000,1220800,1786840,

%T 2529600,3482440,4681600,6166200,7978240,10162600,12767040,15842200,

%U 19441600,23621640,28441600,33963640,40252800,47377000,55407040,64416600

%N Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.

%C Column 7 of A207599.

%H R. H. Hardin, <a href="/A207598/b207598.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 120*n^4 + 40*n^3 - 200*n^2 + 80*n.

%F Conjectures from _Colin Barker_, Jun 25 2018: (Start)

%F G.f.: 40*x*(1 + 35*x + 41*x^2 - 5*x^3) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A207599.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 19 2012