A269146 - OEIS

%I #8 Jan 19 2019 12:08:35

%S 4,80,768,6224,46464,330192,2270592,15251152,100647168,655139152,

%T 4217820672,26911075152,170416738944,1072338720464,6710943646848,

%U 41800542176720,259288295447040,1602497927690832,9871915467776256

%N Number of n X 2 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

%H R. H. Hardin, <a href="/A269146/b269146.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 12*a(n-1) - 38*a(n-2) + 12*a(n-3) - a(n-4) for n>5.

%F Empirical g.f.: 4*x*(1 - x)*(1 + 9*x - x^2 - x^3) / (1 - 6*x + x^2)^2. - _Colin Barker_, Jan 19 2019

%e Some solutions for n=4:

%e ..3..2. .0..0. .2..0. .3..3. .1..0. .1..0. .1..3. .3..1. .0..2. .1..1

%e ..2..0. .2..3. .0..2. .3..3. .1..1. .0..2. .0..1. .1..0. .0..0. .3..3

%e ..1..0. .2..2. .0..3. .1..0. .1..3. .0..0. .0..0. .0..1. .2..3. .3..2

%e ..0..1. .3..3. .2..3. .0..0. .1..0. .1..3. .2..0. .0..2. .3..3. .0..2

%Y Column 2 of A269152.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 20 2016