A281982 - OEIS

%I #8 Feb 20 2019 09:51:21

%S 0,0,2,16,88,432,2008,8992,39200,167552,705440,2934784,12091264,

%T 49416448,200598912,809606656,3251253760,12999782400,51779385856,

%U 205542608896,813446920192,3210502631424,12640023828480,49653803819008

%N Number of n X 2 0..1 arrays with no element unequal to more than four of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A281982/b281982.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) - 20*a(n-2) + 24*a(n-3) - 36*a(n-4) + 16*a(n-5) - 16*a(n-6).

%F Empirical g.f.: 2*x^3 / (1 - 4*x + 2*x^2 - 4*x^3)^2. - _Colin Barker_, Feb 20 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A281988.

%K nonn

%O 1,3

%A _R. H. Hardin_, Feb 04 2017