A207924 - OEIS

%I #8 Mar 06 2018 08:55:02

%S 9,81,144,576,1936,6400,21904,73984,250000,846400,2862864,9684544,

%T 32764176,110838784,374964496,1268499456,4291298064,14517358144,

%U 49111878544,166144281664,562062085264,1901442429184,6432533627536

%N Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 0 and 1 1 1 vertically.

%C Column 4 of A207928.

%C It seems that all terms are squares. - _Colin Barker_, Mar 06 2018

%H R. H. Hardin, <a href="/A207924/b207924.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 3*a(n-2) + 6*a(n-3) - a(n-4) - a(n-6) for n>8.

%F Empirical g.f.: x*(9 + 63*x - 45*x^2 - 9*x^3 - 125*x^4 + 17*x^5 - 7*x^6 + 17*x^7) / ((1 + x + x^2 - x^3)*(1 - 3*x - x^2 - x^3)). - _Colin Barker_, Mar 06 2018

%e Some solutions for n=8:

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

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

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

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

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

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

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

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

%Y Cf. A207928.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 21 2012