A187309 - OEIS

%I #8 Apr 23 2018 14:26:49

%S 210,1472,10262,71836,502545,3516295,24602854,172142801,1204456419,

%T 8427400133,58965241283,412570864570,2886695849049,20197773668299,

%U 141320763334969,988799977661816,6918483687265734,48407582536978550

%N Half the number of (n+2) X 3 binary arrays with each 3 X 3 subblock having sum 3, 4, 5 or 6.

%C Column 1 of A187317.

%H R. H. Hardin, <a href="/A187309/b187309.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 7*a(n-1) + a(n-2) - 6*a(n-3) - 6*a(n-4) - 27*a(n-5)  +90*a(n-6) - 81*a(n-8).

%F Empirical g.f.: x*(210 + 2*x - 252*x^2 - 210*x^3 - 477*x^4 + 2718*x^5 - 324*x^6 - 2592*x^7) / (1 - 7*x - x^2 + 6*x^3 + 6*x^4 + 27*x^5 - 90*x^6 + 81*x^8). - _Colin Barker_, Apr 23 2018

%e Some solutions for 4 X 3 with a(1,1)=0:

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

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

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

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

%Y Cf. A187317.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 08 2011