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A220614 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal and vertical neighbors, without consecutive collinear links.

%I A220614 #6 Jul 23 2025 01:17:46
%S A220614 1,1,1,1,2,1,1,3,3,1,1,5,5,5,1,1,8,11,11,8,1,1,13,21,36,21,13,1,1,21,
%T A220614 43,95,95,43,21,1,1,34,85,281,324,281,85,34,1,1,55,171,781,1277,1277,
%U A220614 781,171,55,1,1,89,341,2245,4673,7041,4673,2245,341,89,1,1,144,683,6336
%N A220614 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal and vertical neighbors, without consecutive collinear links.
%C A220614 Table starts
%C A220614 .1...1....1......1.......1.........1..........1............1.............1
%C A220614 .1...2....3......5.......8........13.........21...........34............55
%C A220614 .1...3....5.....11......21........43.........85..........171...........341
%C A220614 .1...5...11.....36......95.......281........781.........2245..........6336
%C A220614 .1...8...21.....95.....324......1277.......4673........17768.........66245
%C A220614 .1..13...43....281....1277......7041......34981.......183920........937663
%C A220614 .1..21...85....781....4673.....34981.....233265......1653229......11354857
%C A220614 .1..34..171...2245...17768....183920....1653229.....16038658.....149429377
%C A220614 .1..55..341...6336...66245....937663...11354857....149429377....1884307184
%C A220614 .1..89..683..18061..249499...4861869...79290645...1423339849...24310532213
%C A220614 .1.144.1365..51205..934816..24977087..548972737..13397669320..309983079825
%C A220614 .1.233.2731.145601.3511945.128971605.3817993565.126938044289.3977585437731
%H A220614 R. H. Hardin, <a href="/A220614/b220614.txt">Table of n, a(n) for n = 1..544</a>
%e A220614 Some solutions for n=3 k=4 0=self 2=n 4=w 6=e 8=s (reciprocal directions total 10)
%e A220614 .00.00.68.48...68.48.68.48...68.48.00.00...00.00.00.00...00.68.48.00
%e A220614 .00.00.26.24...26.24.26.24...26.24.00.00...00.00.00.00...00.26.24.00
%e A220614 .00.00.00.00...00.00.00.00...00.00.00.00...00.00.00.00...00.00.00.00
%Y A220614 Column 2 is A000045(n+1)
%Y A220614 Column 3 is A001045(n+1)
%Y A220614 Column 4 is A005178(n+1)
%Y A220614 Diagonal is A086832
%K A220614 nonn,tabl
%O A220614 1,5
%A A220614 _R. H. Hardin_ Dec 17 2012