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A220632 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.

%I A220632 #6 Jul 23 2025 01:19:26
%S A220632 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 A220632 257,114,13,1,1,1,64,564,1665,1481,351,21,1,1,1,128,2010,10695,17527,
%U A220632 8560,1081,34,1,1,1,256,7160,68637,201903,183961,49448,3329,55,1,1,1,512
%N A220632 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 A220632 Table starts
%C A220632 .1.1...1......1.........1............1...............1..................1
%C A220632 .1.1...2......4.........8...........16..............32.................64
%C A220632 .1.1...3.....12........44..........158.............564...............2010
%C A220632 .1.1...5.....37.......257.........1665...........10695..............68637
%C A220632 .1.1...8....114......1481........17527..........201903............2329448
%C A220632 .1.1..13....351......8560.......183961.........3817452...........79063898
%C A220632 .1.1..21...1081.....49448......1932695........72097810.........2685329069
%C A220632 .1.1..34...3329....285669.....20301254......1362188752........91163971015
%C A220632 .1.1..55..10252...1650333....213251377.....25734606523......3095401422320
%C A220632 .1.1..89..31572...9534128...2240062837....486186026515....105098157017450
%C A220632 .1.1.144..97229..55079528..23530357757...9185167500820...3568417528948249
%C A220632 .1.1.233.299426.318199485.247170637157.173528846174065.121159087987547537
%H A220632 R. H. Hardin, <a href="/A220632/b220632.txt">Table of n, a(n) for n = 1..287</a>
%e A220632 Some solutions for n=3 k=4 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
%e A220632 .00.67.46.47...00.67.46.47...00.67.47.00...00.00.00.00...00.00.67.47
%e A220632 .36.46.34.00...36.47.36.47...36.34.00.00...00.00.00.00...00.37.36.47
%e A220632 .00.00.00.00...36.46.34.00...00.00.00.00...00.00.00.00...36.46.34.00
%Y A220632 Column 3 is A000045(n+1)
%Y A220632 Column 4 is A099098
%Y A220632 Row 2 is A000079(n-2)
%K A220632 nonn,tabl
%O A220632 1,8
%A A220632 _R. H. Hardin_ Dec 17 2012