A207961 - OEIS

%I #8 Mar 06 2018 08:55:13

%S 6,36,102,281,699,1799,4706,12161,31356,81206,210185,543399,1405547,

%T 3636320,9405751,24328772,62932300,162787659,421078225,1089199555,

%U 2817430618,7287821163,18851338264,48762622760,126133900375,326269518673

%N Number of 3 X n 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 0 vertically.

%C Row 3 of A207960.

%H R. H. Hardin, <a href="/A207961/b207961.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + a(n-2) + 7*a(n-3) + 4*a(n-4) - 7*a(n-6) - 6*a(n-7) + 6*a(n-9) + 2*a(n-10) - a(n-11) - a(n-12) for n>13.

%F Empirical g.f.: x*(6 + 30*x + 60*x^2 + 101*x^3 + 40*x^4 - 39*x^5 - 125*x^6 - 73*x^7 + 30*x^8 + 94*x^9 + 23*x^10 - 19*x^11 - 15*x^12) / ((1 + x^2 - x^3)*(1 - x - 2*x^2 - 5*x^3 - 3*x^4 + 3*x^5 + 5*x^6 - 2*x^8 - x^9)). - _Colin Barker_, Mar 06 2018

%e Some solutions for n=4:

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

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

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

%Y Cf. A207960.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 21 2012