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1/3 the number of n X n 0..2 symmetric matrices with every element equal to zero, one, two or three horizontal and vertical neighbors
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%I #6 Dec 18 2015 18:18:07

%S 1,9,216,15444,3281472,2067554808,3863711228544,21415460458704264,

%T 352065294244909032696,17166897737612437082259600,

%U 2482751631736501357900013730432,1064995044786220639044258688726569096

%N 1/3 the number of n X n 0..2 symmetric matrices with every element equal to zero, one, two or three horizontal and vertical neighbors

%H R. H. Hardin, <a href="/A211044/b211044.txt">Table of n, a(n) for n = 1..16</a>

%e Some solutions for n=4

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_ Mar 30 2012