A281133 - OEIS

%I #8 Feb 16 2019 09:19:09

%S 0,0,24,112,504,2528,11712,52160,230048,1000320,4294016,18264832,

%T 77098880,323290624,1347997696,5593390080,23110676992,95130810368,

%U 390287108096,1596449140736,6512744568832,26504685772800,107628465111040

%N Number of n X 2 0..2 arrays with no element equal to more than one 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="/A281133/b281133.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) - 20*a(n-2) + 32*a(n-3) - 84*a(n-4) + 96*a(n-5) - 96*a(n-6) + 128*a(n-7) - 64*a(n-8).

%F Empirical g.f.: 8*x^3*(1 - x)^2*(3 - 4*x) / (1 - 4*x + 2*x^2 - 8*x^3 + 8*x^4)^2. - _Colin Barker_, Feb 16 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A281139.

%K nonn

%O 1,3

%A _R. H. Hardin_, Jan 15 2017