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Number of lower triangles of an n X n 0..2 array with no element differing from any of its horizontal or vertical neighbors by more than one.
1

%I #9 Jun 20 2022 20:40:00

%S 3,17,217,5873,344091,43337009,11761200209,6872287575297,

%T 8648230733328339,23436303828484483825,136773087470228122215081,

%U 1718926116885238623987854577,46522215573069867474481754034859

%N Number of lower triangles of an n X n 0..2 array with no element differing from any of its horizontal or vertical neighbors by more than one.

%C Column 2 of A194931.

%H R. H. Hardin, <a href="/A194925/b194925.txt">Table of n, a(n) for n = 1..21</a>

%e Some solutions for 4 X 4

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

%e ..1.2......1.0......1.1......1.2......0.1......0.1......1.0......0.1

%e ..2.1.1....1.0.0....0.1.0....2.1.2....1.2.2....1.1.2....0.0.0....0.1.0

%e ..2.2.1.1..0.0.0.0..0.0.0.1..1.2.2.2..1.1.1.2..2.2.1.2..0.1.1.1..1.0.1.1

%Y Cf. A194931.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 05 2011