login
Number of 1 X n 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.
1

%I #8 Feb 13 2019 10:16:48

%S 0,0,2,2,8,14,36,74,168,358,780,1666,3568,7582,16084,33978,71608,

%T 150486,315548,660210,1378688,2873870,5980772,12427562,25787208,

%U 53438534,110605356,228667234,472247568,974321278,2008294900,4135894426

%N Number of 1 X n 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.

%H R. H. Hardin, <a href="/A280399/b280399.txt">Table of n, a(n) for n = 1..210</a>

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

%F Conjectures from _Colin Barker_, Feb 13 2019: (Start)

%F G.f.: 2*x^3*(1 - x - x^2) / ((1 + x)^2*(1 - 2*x)^2).

%F a(n) = (8*((-1)^(1+n)+2^n) + 3*(-8*(-1)^n+2^n)*n) / 108 for n>1.

%F (End)

%e All solutions for n=4:

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

%Y Row 1 of A280398.

%K nonn

%O 1,3

%A _R. H. Hardin_, Jan 02 2017