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T(n,k)=Number of nXk binary arrays with each 1 adjacent to exactly two other 1s
6

%I #5 Mar 31 2012 12:35:50

%S 1,1,1,1,2,1,1,3,3,1,1,4,6,4,1,1,6,10,10,6,1,1,9,19,27,19,9,1,1,13,37,

%T 72,72,37,13,1,1,19,69,179,289,179,69,19,1,1,28,129,447,996,996,447,

%U 129,28,1,1,41,244,1139,3325,4740,3325,1139,244,41,1,1,60,460,2912,11415,21259

%N T(n,k)=Number of nXk binary arrays with each 1 adjacent to exactly two other 1s

%C Table starts

%C .1..1...1....1......1.......1........1.........1..........1...........1

%C .1..2...3....4......6.......9.......13........19.........28..........41

%C .1..3...6...10.....19......37.......69.......129........244.........460

%C .1..4..10...27.....72.....179......447......1139.......2912........7434

%C .1..6..19...72....289.....996.....3325.....11415......39720......138689

%C .1..9..37..179....996....4740....21259.....96524.....443793.....2054180

%C .1.13..69..447...3325...21259...128371....770542....4639132....28160294

%C .1.19.129.1139..11415...96524...770542...6115158...48449560...386449543

%C .1.28.244.2912..39720..443793..4639132..48449560..505971397..5319953708

%C .1.41.460.7434.138689.2054180.28160294.386449543.5319953708.73890230419

%H R. H. Hardin, <a href="/A183328/b183328.txt">Table of n, a(n) for n = 1..391</a>

%e Some solutions for 7X6

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

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

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

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

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

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

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

%Y Column 2 is A000930(n+1)

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_ Jan 03 2011