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%I #7 Aug 03 2018 05:09:02
%S 1,5,22,72,258,949,3403,12241,44192,159272,573952,2069009,7457849,
%T 26881189,96893542,349253376,1258880466,4537629845,16355874451,
%U 58954682593,212501925632,765962408016,2760908604224,9951684619105
%N Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two horizontal, diagonal and antidiagonal neighbors, without consecutive collinear links.
%C Column 3 of A220738.
%H R. H. Hardin, <a href="/A220733/b220733.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + 3*a(n-2) + 9*a(n-3) + 4*a(n-4) - a(n-5).
%F Empirical g.f.: x*(1 + 3*x + 9*x^2 + 4*x^3 - x^4) / (1 - 2*x - 3*x^2 - 9*x^3 - 4*x^4 + x^5). - _Colin Barker_, Aug 03 2018
%e Some solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10):
%e .00.69.47...00.00.00...00.69.47...69.47.00...00.79.00...00.00.00...69.47.00
%e .69.34.17...00.69.47...00.39.17...39.16.47...39.00.17...69.49.00...39.17.00
%e .00.13.00...00.36.14...00.36.14...00.13.00...00.13.00...00.16.14...36.14.00
%Y Cf. A220738.
%K nonn
%O 1,2
%A _R. H. Hardin_, Dec 18 2012
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