A280668 - OEIS

%I #9 Feb 14 2019 07:44:27

%S 4,59,858,12484,181640,2642832,38452768,559481408,8140361856,

%T 118440917248,1723295736320,25073667646464,364817712941056,

%U 5308037322346496,77231064216379392,1123699197608083456

%N Number of n X 3 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A280668/b280668.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 14*a(n-1) + 8*a(n-2).

%F Conjectures from _Colin Barker_, Feb 14 2019: (Start)

%F G.f.: x*(4 + 3*x) / (1 - 14*x - 8*x^2).

%F a(n) = ((7-sqrt(57))^n*(-11+3*sqrt(57)) + (7+sqrt(57))^n*(11+3*sqrt(57))) / (16*sqrt(57)).

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Column 3 of A280673.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 07 2017