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%I #11 Aug 02 2018 06:49:35
%S 1,1,5,13,37,105,298,846,2404,6826,19394,55081,156473,444445,1262497,
%T 3586113,10186570,28935186,82191652,233468038,663174914,1883771569,
%U 5350922525,15199487245,43174696525,122639283705,348361331050
%N Number of ways to reciprocally link elements of a 4 X n array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.
%C Row 4 of A220708.
%H R. H. Hardin, <a href="/A220709/b220709.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + 6*a(n-2) - 6*a(n-4) - a(n-5) + a(n-6) for n>7.
%F Empirical g.f.: x*(1 - 2*x^2 + 2*x^3 - 3*x^5 + x^6) / ((1 - x)*(1 + x)*(1 - x - 5*x^2 - x^3 + x^4)). - _Colin Barker_, Aug 02 2018
%e All solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
%e .00.00.00...00.00.00...00.67.47...00.67.47...00.00.00
%e .00.67.47...00.00.00...36.34.00...36.34.00...00.00.00
%e .36.34.00...00.00.00...00.00.00...00.67.47...00.67.47
%e .00.00.00...00.00.00...00.00.00...36.34.00...36.34.00
%Y Cf. A220708.
%K nonn
%O 1,3
%A _R. H. Hardin_, Dec 18 2012
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