%I #7 Aug 02 2018 06:49:16

%S 1,5,12,37,107,317,932,2749,8101,23881,70392,207497,611639,1802937,

%T 5314536,15665721,46178025,136119501,401241028,1182742829,3486384739,

%U 10276856693,30293209548,89295644789,263217806797,775890178961

%N Number of ways to reciprocally link elements of an n X 5 array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

%C Column 5 of A220708.

%H R. H. Hardin, <a href="/A220705/b220705.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - a(n-4) - 2*a(n-5) - a(n-6).

%F Empirical g.f.: x*(1 + 3*x - x^2 - 2*x^3 - 2*x^4 - x^5) / ((1 - x)*(1 + x)*(1 - 2*x - 2*x^2 - 2*x^3 - x^4)). - _Colin Barker_, Aug 02 2018

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

%e .00.00.67.47.00...00.00.00.00.00...00.00.00.00.00...00.67.47.00.00

%e .00.36.34.67.47...00.67.47.67.47...00.00.00.00.00...36.34.00.00.00

%e .00.00.36.34.00...36.34.36.34.00...00.00.00.00.00...00.00.00.00.00

%Y Cf. A220708.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 18 2012