A279581 - OEIS

A279581

Number of 2 X n 0..2 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%I #7 Feb 11 2019 05:36:20

%S 0,4,36,304,2212,15428,103648,680052,4380964,27829504,174806900,

%T 1087994628,6720111376,41240210276,251687871332,1528700226512,

%U 9246173840644,55718099241732,334660112687936,2004174865390100

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

%H R. H. Hardin, <a href="/A279581/b279581.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 12*a(n-1) - 36*a(n-2) - 22*a(n-3) + 140*a(n-4) - 48*a(n-5) - 121*a(n-6) + 88*a(n-7) - 16*a(n-8).

%F Empirical g.f.: 4*x^2*(1 - x)*(1 - 3*x + x^2)*(1 + x + 4*x^2) / (1 - 6*x + 11*x^3 - 4*x^4)^2. - _Colin Barker_, Feb 11 2019

%e Some solutions for n=4:

%e ..0..1..2..1. .0..0..1..2. .0..1..1..2. .0..0..1..0. .0..1..0..2

%e ..0..1..1..2. .1..0..0..1. .2..1..0..1. .1..0..1..2. .1..1..0..2

%Y Row 2 of A279580.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 15 2016