A207702 - OEIS

%I #8 Jun 25 2018 10:59:06

%S 40,1600,13230,61254,206910,571350,1369900,2956980,5883084,10965220,

%T 19372210,32726250,53222130,83765514,128131680,191146120,278888400,

%U 398920680,560542294,775071790,1056157830,1420120350,1886323380

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

%C Column 7 of A207703.

%H R. H. Hardin, <a href="/A207702/b207702.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: 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).

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

%F G.f.: 2*x*(20 + 640*x + 775*x^2 - 1013*x^3 + 259*x^4 + 31*x^5 - 12*x^6) / (1 - x)^8.

%F a(n) = (n*(162 - 327*n - 881*n^2 + 1296*n^3 + 997*n^4 + 183*n^5 + 10*n^6)) / 36.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A207703.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 19 2012