A269137 - OEIS

%I #10 Jan 19 2019 08:44:39

%S 16,148,1164,8532,59916,408596,2727564,17914580,116170764,745617300,

%T 4745165964,29984668756,188330955276,1176750424852,7319499656844,

%U 45347466532308,279961285570572,1722988944076436,10574188575966348

%N Number of n X 2 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

%H R. H. Hardin, <a href="/A269137/b269137.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*(4 - 11*x - x^2 - x^3 + x^4) / (1 - 6*x + x^2)^2. - _Colin Barker_, Jan 19 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A269143.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 20 2016