A207402 - OEIS

%I #8 Jun 22 2018 08:27:28

%S 20,400,2340,8910,26676,68060,154580,321110,621300,1134296,1972900,

%T 3293310,5306580,8291940,12612116,18730790,27232340,38844000,54460580,

%U 75171886,102292980,137397420,182353620,239364470,311010356,400295720

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

%C Column 7 of A207403.

%H R. H. Hardin, <a href="/A207402/b207402.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/36)*n^7 + (4/9)*n^6 + (53/18)*n^5 + (91/9)*n^4 + (589/36)*n^3 + (31/9)*n^2 - (58/3)*n + 6.

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

%F G.f.: 2*x*(10 + 120*x - 150*x^2 + 135*x^3 - 42*x^4 - 14*x^5 + 14*x^6 - 3*x^7) / (1 - x)^8.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A207403.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 17 2012