cp's OEIS Frontend

A220564 Number of ways to reciprocally link elements of an 3 X n array either to themselves or to exactly one horizontal or antidiagonal neighbor.

%I A220564 #7 Aug 01 2018 04:56:24
%S A220564 1,13,64,430,2604,16310,101052,628269,3901815,24240377,150578968,
%T A220564 935414825,5810847665,36097422853,224239670624,1392992694942,
%U A220564 8653368270212,53755331997318,333931897912068,2074408410086741
%N A220564 Number of ways to reciprocally link elements of an 3 X n array either to themselves or to exactly one horizontal or antidiagonal neighbor.
%C A220564 Row 3 of A220562.
%H A220564 R. H. Hardin, <a href="/A220564/b220564.txt">Table of n, a(n) for n = 1..210</a>
%F A220564 Empirical: a(n) = 4*a(n-1) + 15*a(n-2) - 5*a(n-3) - 19*a(n-4) + 9*a(n-5) + 2*a(n-6) - a(n-7).
%F A220564 Empirical g.f.: x*(1 - x)*(1 + 10*x + 7*x^2 - 9*x^3 - x^4 + x^5) / ((1 + x - x^2)*(1 - 5*x - 9*x^2 + 9*x^3 + x^4 - x^5)). - _Colin Barker_, Aug 01 2018
%e A220564 Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
%e A220564 ..0..6..4....6..4..0....0..7..0....0..7..7....0..6..4....6..4..7....0..0..0
%e A220564 ..6..4..0....0..7..0....3..0..0....3..3..7....0..0..0....0..3..7....6..4..0
%e A220564 ..0..6..4....3..0..0....6..4..0....0..3..0....0..0..0....0..3..0....0..6..4
%Y A220564 Cf. A220562.
%K A220564 nonn
%O A220564 1,2
%A A220564 _R. H. Hardin_, Dec 16 2012