A206989 - OEIS

%I #11 Jun 17 2018 14:36:29

%S 7,49,174,840,3858,17460,80070,365784,1670838,7636416,34893438,

%T 159444240,728589330,3329288484,15213221238,69517022592,317658800982,

%U 1451545657152,6632855083422,30308909178984,138496917825186,632863297956804

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

%C Column 3 of A206994.

%H R. H. Hardin, <a href="/A206989/b206989.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 5*a(n-2) + 11*a(n-3) - 5*a(n-4) + a(n-5) - 3*a(n-6) + a(n-7) for n>9.

%F Empirical g.f.: x*(1 - x)*(7 + 35*x + 27*x^2 + 23*x^3 - 13*x^4 - 3*x^5 - x^6 + x^7) / (1 - 3*x - 5*x^2 - 11*x^3 + 5*x^4 - x^5 + 3*x^6 - x^7). - _Colin Barker_, Jun 17 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A206994.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 14 2012