A208554 - OEIS

%I #8 Sep 27 2018 19:57:31

%S 42,1764,10710,65025,221340,753424,1913940,4862025,10332630,21958596,

%T 41363322,77915929,134523480,232257600,375406920,606784689,931373730,

%U 1429596100,2104920510,3099260241,4409811252,6274540944,8675694300

%N Number of nX7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 0 1 1 vertically

%C Column 7 of A208555

%H R. H. Hardin, <a href="/A208554/b208554.txt">Table of n, a(n) for n = 1..210</a>

%H Robert Israel, <a href="/A208554/a208554.pdf">Maple-assisted proof of formula</a>

%F Empirical: a(n) = 2*a(n-1) +6*a(n-2) -14*a(n-3) -14*a(n-4) +42*a(n-5) +14*a(n-6) -70*a(n-7) +70*a(n-9) -14*a(n-10) -42*a(n-11) +14*a(n-12) +14*a(n-13) -6*a(n-14) -2*a(n-15) +a(n-16).

%F Empirical formula verified (see link). - _Robert Israel_, Sep 27 2018

%e Some solutions for n=4

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Feb 28 2012