A207495 - OEIS

%I #8 Mar 05 2018 05:59:55

%S 6,36,102,297,932,2974,9723,32164,107568,362291,1226924,4170948,

%T 14218841,48567776,166128066,568812225,1948947544,6681079858,

%U 22911053867,78586955264,269607037796,925049643523,3174213970624,10892652172048

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

%C Column 3 of A207500.

%H R. H. Hardin, <a href="/A207495/b207495.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) -2*a(n-2) -14*a(n-3) +6*a(n-4) +8*a(n-5) -a(n-6) -a(n-7) for n>8.

%F Empirical g.f.: x*(6 + 6*x - 66*x^2 - 57*x^3 + 119*x^4 + 72*x^5 - 19*x^6 - 11*x^7) / ((1 - x)*(1 - 2*x - x^2)*(1 - 2*x - 5*x^2 + x^4)). - _Colin Barker_, Mar 05 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A207500.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 18 2012