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 A220706 Number of ways to reciprocally link elements of an n X 6 array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links. 1

%I #7 Aug 02 2018 06:42:39

%S 1,8,24,105,405,1617,6412,25449,101029,400986,1591697,6317904,

%T 25077948,99542634,395117919,1568354512,6225321052,24710371599,

%U 98083689723,389326813396,1545367714146,6134078853549,24348200775585,96646113488531

%N Number of ways to reciprocally link elements of an n X 6 array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

%C Column 6 of A220708.

%H R. H. Hardin, <a href="/A220706/b220706.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 5*a(n-2) - 3*a(n-3) - 6*a(n-4) - a(n-5) - a(n-6) + 4*a(n-7) + a(n-8) - a(n-9) - a(n-10).

%F Empirical g.f.: x*(1 + x)*(1 + 4*x - 9*x^2 + 5*x^3 - 5*x^4 + 3*x^5 + x^6 - x^8) / (1 - 3*x - 5*x^2 + 3*x^3 + 6*x^4 + x^5 + x^6 - 4*x^7 - x^8 + x^9 + x^10). - _Colin Barker_, Aug 02 2018

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

%e .00.00.67.47.67.47...00.00.00.00.67.47...00.00.00.00.00.00...00.00.00.00.00.00

%e .00.36.34.36.34.00...00.67.47.36.34.00...00.00.67.47.67.47...00.00.00.00.00.00

%e .00.00.00.00.00.00...36.34.00.00.00.00...00.36.34.36.34.00...00.00.00.00.00.00

%Y Cf. A220708.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 18 2012

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Last modified June 8 18:04 EDT 2023. Contains 363165 sequences. (Running on oeis4.)