A183388 - OEIS

A183388

Half the number of n X 4 binary arrays with no element unequal to a strict majority of its king-move neighbors.

%I #8 Mar 28 2018 08:13:33

%S 2,2,2,4,8,16,36,74,156,334,706,1504,3204,6828,14576,31128,66524,

%T 142262,304360,651456,1394894,2987672,6400950,13716916,29400542,

%U 63027304,135134330,289772558,621434722,1332826866,2858815828,6132363430

%N Half the number of n X 4 binary arrays with no element unequal to a strict majority of its king-move neighbors.

%C Column 4 of A183391.

%H R. H. Hardin, <a href="/A183388/b183388.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - a(n-3) - 4*a(n-4) - 3*a(n-5) - a(n-6) - a(n-7) + 2*a(n-8) for n>9.

%F Empirical g.f.: 2*x*(1 - x - 3*x^2 - x^3 + 3*x^4 + 4*x^5 + 4*x^6 + 2*x^7 - 2*x^8) / (1 - 2*x - 2*x^2 + x^3 + 4*x^4 + 3*x^5 + x^6 + x^7 - 2*x^8). - _Colin Barker_, Mar 28 2018

%e Some solutions with a(1,1)=0 for 5 X 4:

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

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

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

%Y Cf. A183391.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 04 2011