cp's OEIS Frontend

A220616 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor.

%I A220616 #8 Aug 01 2018 14:29:48
%S A220616 3,21,125,765,4657,28373,172833,1052829,6413369,39067429,237981569,
%T A220616 1449678893,8830805161,53793374581,327685538769,1996115937021,
%U A220616 12159458878905,74070066514885,451202212873441,2748525099013581
%N A220616 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor.
%C A220616 Column 3 of A220621.
%H A220616 R. H. Hardin, <a href="/A220616/b220616.txt">Table of n, a(n) for n = 1..210</a>
%F A220616 Empirical: a(n) = 7*a(n-1) - 4*a(n-2) - 10*a(n-3) + 4*a(n-4).
%F A220616 Empirical g.f.: x*(1 + 2*x)*(3 - 6*x + 2*x^2) / (1 - 7*x + 4*x^2 + 10*x^3 - 4*x^4). - _Colin Barker_, Aug 01 2018
%e A220616 Some solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10):
%e A220616 ..0..6..4....0..7..0....0..7..0....0..0..0....6..4..0....0..6..4....0..9..7
%e A220616 ..0..6..4....3..6..4....3..7..7....0..9..7....0..7..0....6..4..0....0..3..1
%e A220616 ..0..0..0....0..6..4....3..3..0....0..3..1....3..0..0....6..4..0....6..4..0
%Y A220616 Cf. A220621.
%K A220616 nonn
%O A220616 1,1
%A A220616 _R. H. Hardin_, Dec 17 2012