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A220602 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.

%I A220602 #6 Jul 23 2025 01:17:25
%S A220602 1,1,1,1,2,1,1,7,7,1,1,17,65,17,1,1,44,471,471,44,1,1,117,3469,9047,
%T A220602 3469,117,1,1,305,25747,167614,167614,25747,305,1,1,798,190425,
%U A220602 3174778,7558495,3174778,190425,798,1,1,2091,1408823,60138423,352586943
%N A220602 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.
%C A220602 Table starts
%C A220602 .1.....1..........1...............1...................1
%C A220602 .1.....2..........7..............17..................44
%C A220602 .1.....7.........65.............471................3469
%C A220602 .1....17........471............9047..............167614
%C A220602 .1....44.......3469..........167614.............7558495
%C A220602 .1...117......25747.........3174778...........352586943
%C A220602 .1...305.....190425........60138423.........16505365334
%C A220602 .1...798....1408823......1137615308........770615995060
%C A220602 .1..2091...10424813.....21523535122......35978245868462
%C A220602 .1..5473...77135267....407249783145....1680090131446571
%C A220602 .1.14328..570740149...7705461280893...78453960278374893
%C A220602 .1.37513.4223043591.145792738613760.3663456651896335065
%H A220602 R. H. Hardin, <a href="/A220602/b220602.txt">Table of n, a(n) for n = 1..180</a>
%e A220602 Some solutions for n=3 k=4 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
%e A220602 .00.68.48.78...00.68.48.00...00.00.67.47...00.67.47.00...00.67.47.00
%e A220602 .68.24.23.28...68.24.28.00...00.38.36.48...36.34.67.47...38.37.68.48
%e A220602 .26.46.46.24...26.46.24.00...00.26.46.24...00.36.34.00...23.00.26.24
%Y A220602 Column 2 is A108479
%K A220602 nonn,tabl
%O A220602 1,5
%A A220602 _R. H. Hardin_ Dec 16 2012