A269271 - OEIS

%I #10 Jan 20 2019 23:18:00

%S 24,1368,46872,1365336,36673560,938176344,23230366488,561939624792,

%T 13356872620056,313173275509080,7262896745936664,166932248829835608,

%U 3808216985895026712,86327991673633618776,1946351959512905208600

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

%H R. H. Hardin, <a href="/A269271/b269271.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 42*a(n-1) - 441*a(n-2).

%F Conjectures from _Colin Barker_, Jan 20 2019: (Start)

%F G.f.: 24*x*(1 + 15*x) / (1 - 21*x)^2.

%F a(n) = 8*3^n * 7^(n-2) * (12*n-5).

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Column 3 of A269276.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 21 2016