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A185540 T(n,k)=1/6 the number of nXk 0..5 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

%I A185540 #9 Jul 22 2025 09:53:56
%S A185540 0,1,1,1,11,1,6,110,110,6,11,1155,2990,1155,11,41,12105,127570,127570,
%T A185540 12105,41,96,127190,4403225,17526450,4403225,127190,96,301,1336205,
%U A185540 167398110,2241330570,2241330570,167398110,1336205,301,781,14039455
%N A185540 T(n,k)=1/6 the number of nXk 0..5 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.
%C A185540 Table starts
%C A185540 ....0.........1............1..............6..............11..............41
%C A185540 ....1........11..........110...........1155...........12105..........127190
%C A185540 ....1.......110.........2990.........127570.........4403225.......167398110
%C A185540 ....6......1155.......127570.......17526450......2241330570....295044602325
%C A185540 ...11.....12105......4403225.....2241330570....994633804270.468362874353295
%C A185540 ...41....127190....167398110...295044602325.468362874353295
%C A185540 ...96...1336205...6079401960.38418831900875
%C A185540 ..301..14039455.225574291125
%C A185540 ..781.147510990
%C A185540 .2286
%H A185540 R. H. Hardin, <a href="/A185540/b185540.txt">Table of n, a(n) for n = 1..59</a>
%e A185540 Some solutions for 4X3 with a(1,1)=0
%e A185540 ..0..1..1....0..0..1....0..0..2....0..0..1....0..0..1....0..4..4....0..0..0
%e A185540 ..0..0..5....5..5..1....4..0..2....3..4..1....0..4..1....0..3..3....0..1..0
%e A185540 ..1..5..5....0..2..4....4..4..3....3..4..1....4..4..0....1..0..0....0..1..0
%e A185540 ..1..4..4....0..2..4....1..1..3....3..4..4....2..2..0....1..3..3....0..5..5
%Y A185540 Column 1 is A015440(n-2)
%K A185540 nonn,tabl
%O A185540 1,5
%A A185540 _R. H. Hardin_ Jan 30 2011