cp's OEIS Frontend

A220629 Number of ways to reciprocally link elements of an n X 5 array either to themselves or to exactly two horizontal or antidiagonal neighbors.

%I A220629 #8 Aug 01 2018 14:29:41
%S A220629 1,8,44,257,1481,8560,49448,285669,1650333,9534128,55079528,318199485,
%T A220629 1838267585,10619840324,61351790884,354434918989,2047603011865,
%U A220629 11829190267612,68338316351600,394796716945057,2280776817922653
%N A220629 Number of ways to reciprocally link elements of an n X 5 array either to themselves or to exactly two horizontal or antidiagonal neighbors.
%C A220629 Column 5 of A220632.
%H A220629 R. H. Hardin, <a href="/A220629/b220629.txt">Table of n, a(n) for n = 1..210</a>
%F A220629 Empirical: a(n) = 4*a(n-1) + 9*a(n-2) + 7*a(n-3) + 2*a(n-4) - a(n-5).
%F A220629 Empirical g.f.: x*(1 + 3*x - x^2)*(1 + x + x^2) / ((1 + x)*(1 - 5*x - 4*x^2 - 3*x^3 + x^4)). - _Colin Barker_, Aug 01 2018
%e A220629 Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
%e A220629 .00.67.46.46.47...00.67.46.47.00...00.00.00.00.00...00.00.67.46.47
%e A220629 .36.47.00.36.47...36.46.34.67.47...00.67.46.47.00...00.37.67.34.00
%e A220629 .36.46.46.34.00...00.00.36.34.00...36.46.34.00.00...36.34.00.00.00
%Y A220629 Cf. A220632.
%K A220629 nonn
%O A220629 1,2
%A A220629 _R. H. Hardin_, Dec 17 2012