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%I #7 Jul 28 2022 03:25:33
%S 0,1,8,156,7480,898680,266674964,196750879896,360466213243792,
%T 1640421325318165822,18541481770815952051304,
%U 520535380394250894532873968,36296751650483051319011293939152
%N 1/3 the number of n X n 0..2 symmetric matrices with every element equal to one, two or three horizontal and vertical neighbors.
%e Some solutions for n=4
%e ..2..2..1..1....1..1..0..1....0..0..1..2....2..2..1..1....2..2..1..1
%e ..2..2..1..0....1..0..0..1....0..1..1..2....2..2..0..2....2..1..1..1
%e ..1..1..1..0....0..0..2..2....1..1..2..2....1..0..0..2....1..1..0..0
%e ..1..0..0..0....1..1..2..2....2..2..2..2....1..2..2..2....1..1..0..0
%K nonn
%O 1,3
%A _R. H. Hardin_, Mar 30 2012
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