cp's OEIS Frontend

A220709 Number of ways to reciprocally link elements of a 4 X n array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

%I A220709 #11 Aug 02 2018 06:49:35
%S A220709 1,1,5,13,37,105,298,846,2404,6826,19394,55081,156473,444445,1262497,
%T A220709 3586113,10186570,28935186,82191652,233468038,663174914,1883771569,
%U A220709 5350922525,15199487245,43174696525,122639283705,348361331050
%N A220709 Number of ways to reciprocally link elements of a 4 X n array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.
%C A220709 Row 4 of A220708.
%H A220709 R. H. Hardin, <a href="/A220709/b220709.txt">Table of n, a(n) for n = 1..210</a>
%F A220709 Empirical: a(n) = a(n-1) + 6*a(n-2) - 6*a(n-4) - a(n-5) + a(n-6) for n>7.
%F A220709 Empirical g.f.: x*(1 - 2*x^2 + 2*x^3 - 3*x^5 + x^6) / ((1 - x)*(1 + x)*(1 - x - 5*x^2 - x^3 + x^4)). - _Colin Barker_, Aug 02 2018
%e A220709 All solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
%e A220709 .00.00.00...00.00.00...00.67.47...00.67.47...00.00.00
%e A220709 .00.67.47...00.00.00...36.34.00...36.34.00...00.00.00
%e A220709 .36.34.00...00.00.00...00.00.00...00.67.47...00.67.47
%e A220709 .00.00.00...00.00.00...00.00.00...36.34.00...36.34.00
%Y A220709 Cf. A220708.
%K A220709 nonn
%O A220709 1,3
%A A220709 _R. H. Hardin_, Dec 18 2012