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A241130 T(n,k)=Number of nXk 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order.

%I A241130 #6 Jul 23 2025 11:11:19
%S A241130 1,2,2,4,9,4,11,54,54,11,30,325,723,325,30,82,1965,9773,9773,1965,82,
%T A241130 224,11876,132369,295584,132369,11876,224,612,71793,1792237,8974020,
%U A241130 8974020,1792237,71793,612,1672,434007,24269723,272418756,611547441,272418756
%N A241130 T(n,k)=Number of nXk 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order.
%C A241130 Table starts
%C A241130 ....1........2...........4..............11................30.................82
%C A241130 ....2........9..........54.............325..............1965..............11876
%C A241130 ....4.......54.........723............9773............132369............1792237
%C A241130 ...11......325........9773..........295584...........8974020..........272418756
%C A241130 ...30.....1965......132369.........8974020.........611547441........41661463219
%C A241130 ...82....11876.....1792237.......272418756.......41661463219......6369134821236
%C A241130 ..224....71793....24269723......8270609664.....2838552905280....973866422990563
%C A241130 ..612...434007...328645291....251096788713...193403197619803.148910067386335603
%C A241130 .1672..2623694..4450319537...7623351508315.13177423185201303
%C A241130 .4568.15861001.60263615333.231446775293031
%H A241130 R. H. Hardin, <a href="/A241130/b241130.txt">Table of n, a(n) for n = 1..97</a>
%F A241130 Empirical for column k:
%F A241130 k=1: a(n) = 2*a(n-1) +2*a(n-2) for n>4
%F A241130 k=2: a(n) = 6*a(n-1) +2*a(n-2) -9*a(n-3) -10*a(n-4) +8*a(n-5) for n>6
%F A241130 k=3: [order 26]
%e A241130 Some solutions for n=3 k=4
%e A241130 ..0..1..0..2....0..1..1..2....0..0..1..0....0..1..0..1....0..1..0..1
%e A241130 ..1..0..2..2....0..2..2..0....1..1..2..0....0..2..1..2....2..2..1..2
%e A241130 ..0..0..0..2....2..1..1..0....0..2..1..2....2..1..0..2....1..1..2..0
%Y A241130 Column 1 is A021006(n-3)
%K A241130 nonn,tabl
%O A241130 1,2
%A A241130 _R. H. Hardin_, Apr 16 2014