A207401 - OEIS

%I #8 Jun 22 2018 08:27:36

%S 16,256,1296,4356,11664,26896,55696,106276,190096,322624,524176,

%T 820836,1245456,1838736,2650384,3740356,5180176,7054336,9461776,

%U 12517444,16353936,21123216,26998416,34175716,42876304,53348416,65869456,80748196

%N Number of n X 6 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.

%C Column 6 of A207403.

%H R. H. Hardin, <a href="/A207401/b207401.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/9)*n^6 + (4/3)*n^5 + (58/9)*n^4 + (40/3)*n^3 + (49/9)*n^2 - (44/3)*n + 4.

%F Conjectures from _Colin Barker_, Jun 22 2018: (Start)

%F G.f.: 4*x*(4 + 36*x - 40*x^2 + 25*x^3 - 3*x^4 - 3*x^5 + x^6) / (1 - x)^7.

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A207403.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 17 2012