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A185409 T(n,k)=1/7 the number of nXk 0..6 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

%I A185409 #13 Jul 22 2025 09:45:47
%S A185409 0,1,1,1,13,1,7,150,150,7,13,1848,5040,1848,13,55,22656,279918,279918,
%T A185409 22656,55,133,278832,12205368,53808534,12205368,278832,133,463,
%U A185409 3430776,595974240,9560464068,9560464068,595974240,3430776,463,1261,42221928
%N A185409 T(n,k)=1/7 the number of nXk 0..6 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.
%C A185409 Table starts
%C A185409 ....0........1...........1.............7............13............55
%C A185409 ....1.......13.........150..........1848.........22656........278832
%C A185409 ....1......150........5040........279918......12205368.....595974240
%C A185409 ....7.....1848......279918......53808534....9560464068.1755419411964
%C A185409 ...13....22656....12205368....9560464068.6409594156632
%C A185409 ...55...278832...595974240.1755419411964
%C A185409 ..133..3430776.27536905674
%C A185409 ..463.42221928
%C A185409 .1261
%H A185409 R. H. Hardin, <a href="/A185409/b185409.txt">Table of n, a(n) for n = 1..49</a>
%e A185409 Some solutions for 4X3 with a(1,1)=0
%e A185409 ..0..3..6....0..0..0....0..0..4....0..0..3....0..3..6....0..3..3....0..0..0
%e A185409 ..0..3..6....4..4..4....0..4..4....3..3..3....0..3..6....0..2..2....4..4..4
%e A185409 ..2..4..4....1..5..4....0..5..5....3..2..2....5..0..6....1..1..1....5..5..6
%e A185409 ..2..2..2....1..5..5....4..4..4....1..1..1....5..0..6....6..6..6....0..0..6
%Y A185409 Column 1 is A015441(n-1)
%K A185409 nonn,tabl
%O A185409 1,5
%A A185409 _R. H. Hardin_ Jan 26 2011