cp's OEIS Frontend

A220710 Number of ways to reciprocally link elements of an 5 X n array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

%I A220710 #7 Aug 02 2018 08:41:02
%S A220710 1,1,8,28,107,405,1520,5706,21418,80390,301736,1132543,4250895,
%T A220710 15955408,59887275,224782132,843701335,3166765105,11886195940,
%U A220710 44613876758,167454575870,628527215306,2359126067724,8854788952291,33235734276043
%N A220710 Number of ways to reciprocally link elements of an 5 X n array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.
%C A220710 Row 5 of A220708.
%H A220710 R. H. Hardin, <a href="/A220710/b220710.txt">Table of n, a(n) for n = 1..210</a>
%F A220710 Empirical: a(n) = 3*a(n-1) + 7*a(n-2) - 14*a(n-3) - 11*a(n-4) + 17*a(n-5) + 5*a(n-6) - 6*a(n-7) for n>11.
%F A220710 Empirical g.f.: x*(1 - 2*x - 2*x^2 + 11*x^3 - 8*x^4 - 6*x^5 + 14*x^6 - 18*x^7 - 3*x^8 + 18*x^9 - 8*x^10) / ((1 - x)*(1 + x)*(1 - 3*x - 6*x^2 + 11*x^3 + 5*x^4 - 6*x^5)). - _Colin Barker_, Aug 02 2018
%e A220710 Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
%e A220710 .00.00.00...00.00.00...00.67.47...00.67.47...00.00.00...00.00.00...00.00.00
%e A220710 .00.67.47...00.00.00...36.34.00...36.34.00...00.00.00...00.67.47...00.00.00
%e A220710 .36.34.00...00.00.00...00.00.00...00.00.00...00.67.47...36.34.00...00.00.00
%e A220710 .00.00.00...00.67.47...00.00.00...00.67.47...36.34.00...00.67.47...00.00.00
%e A220710 .00.00.00...36.34.00...00.00.00...36.34.00...00.00.00...36.34.00...00.00.00
%Y A220710 Cf. A220708.
%K A220710 nonn
%O A220710 1,3
%A A220710 _R. H. Hardin_, Dec 18 2012