A280955 - OEIS

%I #9 Feb 15 2019 04:29:38

%S 2,9,42,205,997,4850,23593,114769,558298,2715861,13211405,64267362,

%T 312630929,1520804569,7398009354,35987886621,175064388469,

%U 851607109714,4142673879353,20152188344737,98031056006074,476875651282597

%N Number of n X 2 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A280955/b280955.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(1 - x)*(1 + x)*(2 + x) / (1 - 4*x - 4*x^2 - x^3). - _Colin Barker_, Feb 15 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A280961.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 11 2017