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T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal or antidiagonal neighbors
10

%I #4 Dec 17 2012 09:31:31

%S 1,1,1,1,1,1,1,2,1,1,1,4,3,1,1,1,8,12,5,1,1,1,16,44,37,8,1,1,1,32,158,

%T 257,114,13,1,1,1,64,564,1665,1481,351,21,1,1,1,128,2010,10695,17527,

%U 8560,1081,34,1,1,1,256,7160,68637,201903,183961,49448,3329,55,1,1,1,512

%N T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal or antidiagonal neighbors

%C Table starts

%C .1.1...1......1.........1............1...............1..................1

%C .1.1...2......4.........8...........16..............32.................64

%C .1.1...3.....12........44..........158.............564...............2010

%C .1.1...5.....37.......257.........1665...........10695..............68637

%C .1.1...8....114......1481........17527..........201903............2329448

%C .1.1..13....351......8560.......183961.........3817452...........79063898

%C .1.1..21...1081.....49448......1932695........72097810.........2685329069

%C .1.1..34...3329....285669.....20301254......1362188752........91163971015

%C .1.1..55..10252...1650333....213251377.....25734606523......3095401422320

%C .1.1..89..31572...9534128...2240062837....486186026515....105098157017450

%C .1.1.144..97229..55079528..23530357757...9185167500820...3568417528948249

%C .1.1.233.299426.318199485.247170637157.173528846174065.121159087987547537

%H R. H. Hardin, <a href="/A220632/b220632.txt">Table of n, a(n) for n = 1..287</a>

%e Some solutions for n=3 k=4 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)

%e .00.67.46.47...00.67.46.47...00.67.47.00...00.00.00.00...00.00.67.47

%e .36.46.34.00...36.47.36.47...36.34.00.00...00.00.00.00...00.37.36.47

%e .00.00.00.00...36.46.34.00...00.00.00.00...00.00.00.00...36.46.34.00

%Y Column 3 is A000045(n+1)

%Y Column 4 is A099098

%Y Row 2 is A000079(n-2)

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_ Dec 17 2012