A208378 - OEIS

%I #8 Jul 02 2018 08:37:36

%S 42,1764,6216,13860,25200,40740,60984,86436,117600,154980,199080,

%T 250404,309456,376740,452760,538020,633024,738276,854280,981540,

%U 1120560,1271844,1435896,1613220,1804320,2009700,2229864,2465316,2716560,2984100,3268440

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

%C Column 7 of A208379.

%H R. H. Hardin, <a href="/A208378/b208378.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 84*n^3 + 840*n^2 - 1344*n + 420 for n>1.

%F Conjectures from _Colin Barker_, Jul 02 2018: (Start)

%F G.f.: 42*x*(1 + 38*x - 14*x^2 - 14*x^3 + x^4) / (1 - x)^4.

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

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A208379.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 25 2012