A280400 - OEIS

A280400

Number of 2Xn 0..2 arrays with no element unequal 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 #6 Jan 04 2017 13:28:34

%S 0,2,6,16,34,76,158,336,698,1460,3030,6296,13042,27004,55822,115296,

%T 237866,490308,1009734,2077736,4271970,8776972,18019966,36972016,

%U 75808154,155344596,318145718,651204536,1332235218,2724122780,5567550190

%N Number of 2Xn 0..2 arrays with no element unequal 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.

%C Row 2 of A280398.

%H R. H. Hardin, <a href="/A280400/b280400.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +a(n-2) -7*a(n-3) +4*a(n-5).

%F Empirical g.f.: 2*x^2*(-1+2*x^2+3*x^3) / ( (x-1)*(1+x)^2*(2*x-1)^2 ). - _R. J. Mathar_, Jan 04 2017

%F Empirical: a(n) = 2^(n-1)*n/9 +2^(n-1)*47/27 +(-1)^n*2*n/9 -10*(-1)^n/27-2. - _R. J. Mathar_, Jan 04 2017

%e Some solutions for n=4

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

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

%Y Cf. A280398.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 02 2017