A268900 - OEIS

%I #8 Jan 16 2019 09:23:37

%S 36,696,9720,118584,1347192,14644152,154472184,1594323000,16185567096,

%T 162200044728,1608569870328,15816054042936,154394813276280,

%U 1498006261495224,14458132831535352,138907883786523192

%N Number of n X 4 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

%H R. H. Hardin, <a href="/A268900/b268900.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 18*a(n-1) - 81*a(n-2) for n>3.

%F Conjectures from _Colin Barker_, Jan 16 2019: (Start)

%F G.f.: 12*x*(3 + 4*x + 9*x^2) / (1 - 9*x)^2.

%F a(n) = 8 * 3^(2*n-3) * (16*n-3) for n>1.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Column 4 of A268904.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 15 2016