A279128 - OEIS

%I #9 Feb 26 2018 07:29:01

%S 1,0,9,34,87,194,400,790,1511,2830,5213,9484,17080,30508,54117,95434,

%T 167443,292486,508912,882402,1525219,2628886,4519577,7751888,13267384,

%U 22662360,38639553,65769394,111771663,189671306,321421456,543987118

%N Number of n X 2 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

%C Column 2 of A279134.

%H R. H. Hardin, <a href="/A279128/b279128.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 7*a(n-2) - 2*a(n-3) + 10*a(n-4) - 2*a(n-5) - 5*a(n-6) + a(n-7) + a(n-8) for n>9.

%F Empirical g.f.: x*(1 - 5*x + 16*x^2 - 9*x^3 - 30*x^4 + 17*x^5 + 22*x^6 - x^7 - 9*x^8) / ((1 - x)^2*(1 - x - x^2)^3). - _Colin Barker_, Feb 26 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A279134.

%K nonn

%O 1,3

%A _R. H. Hardin_, Dec 06 2016