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A220708 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

%I A220708 #6 Jul 23 2025 01:22:24
%S A220708 1,1,1,1,1,1,1,2,1,1,1,3,3,1,1,1,5,6,5,1,1,1,8,12,13,8,1,1,1,13,24,37,
%T A220708 28,13,1,1,1,21,48,105,107,60,21,1,1,1,34,96,298,405,317,129,34,1,1,1,
%U A220708 55,192,846,1520,1617,932,277,55,1,1,1,89,384,2404,5706,8338,6412,2749,595
%N A220708 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.
%C A220708 Table starts
%C A220708 .1.1...1....1......1.......1.........1..........1............1.............1
%C A220708 .1.1...2....3......5.......8........13.........21...........34............55
%C A220708 .1.1...3....6.....12......24........48.........96..........192...........384
%C A220708 .1.1...5...13.....37.....105.......298........846.........2404..........6826
%C A220708 .1.1...8...28....107.....405......1520.......5706........21418.........80390
%C A220708 .1.1..13...60....317....1617......8338......42873.......221082.......1139020
%C A220708 .1.1..21..129....932....6412.....44976.....311193......2168111......15034974
%C A220708 .1.1..34..277...2749...25449....244029....2282408.....21692285.....204339688
%C A220708 .1.1..55..595...8101..101029...1322551...16699080....216083336....2751764573
%C A220708 .1.1..89.1278..23881..400986...7171769..122254180...2156218093...37166744488
%C A220708 .1.1.144.2745..70392.1591697..38885648..894932114..21512078437..501632637139
%C A220708 .1.1.233.5896.207497.6317904.210854845.6551231662.214655813486.6771890123950
%H A220708 R. H. Hardin, <a href="/A220708/b220708.txt">Table of n, a(n) for n = 1..391</a>
%e A220708 Some solutions for n=3 k=4 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
%e A220708 .00.67.47.00...00.00.00.00...00.00.67.47...00.00.00.00...00.67.47.00
%e A220708 .36.34.00.00...00.00.00.00...00.36.34.00...00.00.67.47...36.34.67.47
%e A220708 .00.00.00.00...00.00.00.00...00.00.00.00...00.36.34.00...00.36.34.00
%Y A220708 Column 3 is A000045(n+1)
%Y A220708 Column 4 is A002478
%Y A220708 Row 2 is A000045
%Y A220708 Row 3 is A003945(n-2)
%K A220708 nonn,tabl
%O A220708 1,8
%A A220708 _R. H. Hardin_ Dec 18 2012