A220597 - OEIS

%I #7 Aug 01 2018 05:52:26

%S 1,7,65,471,3469,25747,190425,1408823,10424813,77135267,570740149,

%T 4223043591,31247282909,231205914319,1710746473929,12658211881263,

%U 93661059763965,693020010391803,5127816575062977,37941909947454471

%N Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.

%C Column 3 of A220602.

%H R. H. Hardin, <a href="/A220597/b220597.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) + 7*a(n-2) + 25*a(n-3) - 3*a(n-4) + 9*a(n-5) + 22*a(n-6) - 5*a(n-7) - 2*a(n-8).

%F Empirical g.f.: x*(1 + x + 16*x^2 + 7*x^3 + 16*x^4 + 23*x^5 - 5*x^6 - 2*x^7) / ((1 - x + x^2)*(1 - 5*x - 13*x^2 - 33*x^3 - 17*x^4 + 7*x^5 + 2*x^6)). - _Colin Barker_, Aug 01 2018

%e Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10):

%e .68.46.48...00.67.47...00.68.48...00.68.48...00.67.47...68.46.47...00.00.78

%e .28.68.24...38.36.48...68.24.27...00.27.28...38.38.00...26.34.00...68.34.28

%e .26.24.00...26.46.24...26.34.00...36.46.24...26.24.00...00.00.00...26.46.24

%Y Cf. A220602.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 16 2012