A269284 - OEIS

%I #8 Jan 21 2019 06:12:42

%S 60,2124,62748,1698732,43674876,1085203980,26317946844,626778812268,

%T 14718495557052,341767357185996,7863372461151900,179542238849355564,

%U 4073026776304945788,91888997272241919372,2063133077083679521116

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

%H R. H. Hardin, <a href="/A269284/b269284.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 21 2019: (Start)

%F G.f.: 12*x*(5 - 33*x) / (1 - 21*x)^2.

%F a(n) = 4 * 3^n * 7^(n-2) * (24*n+11).

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Column 3 of A269289.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 21 2016