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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 9

%I

%S 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 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 55,192,846,1520,1617,932,277,55,1,1,1,89,384,2404,5706,8338,6412,2749,595

%N 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 Table starts

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

%C .1.1...2....3......5.......8........13.........21...........34............55

%C .1.1...3....6.....12......24........48.........96..........192...........384

%C .1.1...5...13.....37.....105.......298........846.........2404..........6826

%C .1.1...8...28....107.....405......1520.......5706........21418.........80390

%C .1.1..13...60....317....1617......8338......42873.......221082.......1139020

%C .1.1..21..129....932....6412.....44976.....311193......2168111......15034974

%C .1.1..34..277...2749...25449....244029....2282408.....21692285.....204339688

%C .1.1..55..595...8101..101029...1322551...16699080....216083336....2751764573

%C .1.1..89.1278..23881..400986...7171769..122254180...2156218093...37166744488

%C .1.1.144.2745..70392.1591697..38885648..894932114..21512078437..501632637139

%C .1.1.233.5896.207497.6317904.210854845.6551231662.214655813486.6771890123950

%H R. H. Hardin, <a href="/A220708/b220708.txt">Table of n, a(n) for n = 1..391</a>

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

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

%e .36.34.00.00...00.00.00.00...00.36.34.00...00.00.67.47...36.34.67.47

%e .00.00.00.00...00.00.00.00...00.00.00.00...00.36.34.00...00.36.34.00

%Y Column 3 is A000045(n+1)

%Y Column 4 is A002478

%Y Row 2 is A000045

%Y Row 3 is A003945(n-2)

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_ Dec 18 2012

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Last modified June 21 08:56 EDT 2021. Contains 345358 sequences. (Running on oeis4.)