A220611 - OEIS

%I #9 Aug 01 2018 14:29:44

%S 1,8,21,95,324,1277,4673,17768,66245,249499,934816,3511945,13175625,

%T 49465544,185641901,696836263,2615432756,9816980965,36846924297,

%U 138302568456,519106314333,1948425878179,7313254531824,27449718110385

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

%C Column 5 of A220614.

%H R. H. Hardin, <a href="/A220611/b220611.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 6*a(n-2) - 11*a(n-3) - 5*a(n-4) + 6*a(n-5).

%F Empirical g.f.: x*(1 + 5*x - 9*x^2 - 5*x^3 + 6*x^4) / (1 - 3*x - 6*x^2 + 11*x^3 + 5*x^4 - 6*x^5). - _Colin Barker_, Aug 01 2018

%e Some solutions for n=3 0=self 2=n 4=w 6=e 8=s (reciprocal directions total 10):

%e .00.00.00.00.00...00.00.68.48.00...68.48.00.00.00...00.00.00.00.00

%e .68.48.00.68.48...68.48.26.24.00...26.24.68.48.00...00.00.00.68.48

%e .26.24.00.26.24...26.24.00.00.00...00.00.26.24.00...00.00.00.26.24

%Y Cf. A220614.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 17 2012