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Number of ways to reciprocally link elements of an n X 5 array either to themselves or to exactly two horizontal or antidiagonal neighbors.
1

%I #8 Aug 01 2018 14:29:41

%S 1,8,44,257,1481,8560,49448,285669,1650333,9534128,55079528,318199485,

%T 1838267585,10619840324,61351790884,354434918989,2047603011865,

%U 11829190267612,68338316351600,394796716945057,2280776817922653

%N 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 Column 5 of A220632.

%H R. H. Hardin, <a href="/A220629/b220629.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 9*a(n-2) + 7*a(n-3) + 2*a(n-4) - a(n-5).

%F 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 Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):

%e .00.67.46.46.47...00.67.46.47.00...00.00.00.00.00...00.00.67.46.47

%e .36.47.00.36.47...36.46.34.67.47...00.67.46.47.00...00.37.67.34.00

%e .36.46.46.34.00...00.00.36.34.00...36.46.34.00.00...36.34.00.00.00

%Y Cf. A220632.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 17 2012