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 A220710 Number of ways to reciprocally link elements of an 5 X n array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links. 1

%I #7 Aug 02 2018 08:41:02

%S 1,1,8,28,107,405,1520,5706,21418,80390,301736,1132543,4250895,

%T 15955408,59887275,224782132,843701335,3166765105,11886195940,

%U 44613876758,167454575870,628527215306,2359126067724,8854788952291,33235734276043

%N Number of ways to reciprocally link elements of an 5 X n array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

%C Row 5 of A220708.

%H R. H. Hardin, <a href="/A220710/b220710.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 7*a(n-2) - 14*a(n-3) - 11*a(n-4) + 17*a(n-5) + 5*a(n-6) - 6*a(n-7) for n>11.

%F Empirical g.f.: x*(1 - 2*x - 2*x^2 + 11*x^3 - 8*x^4 - 6*x^5 + 14*x^6 - 18*x^7 - 3*x^8 + 18*x^9 - 8*x^10) / ((1 - x)*(1 + x)*(1 - 3*x - 6*x^2 + 11*x^3 + 5*x^4 - 6*x^5)). - _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 .00.00.00...00.00.00...00.67.47...00.67.47...00.00.00...00.00.00...00.00.00

%e .00.67.47...00.00.00...36.34.00...36.34.00...00.00.00...00.67.47...00.00.00

%e .36.34.00...00.00.00...00.00.00...00.00.00...00.67.47...36.34.00...00.00.00

%e .00.00.00...00.67.47...00.00.00...00.67.47...36.34.00...00.67.47...00.00.00

%e .00.00.00...36.34.00...00.00.00...36.34.00...00.00.00...36.34.00...00.00.00

%Y Cf. A220708.

%K nonn

%O 1,3

%A _R. H. Hardin_, Dec 18 2012

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Last modified May 30 03:43 EDT 2023. Contains 363044 sequences. (Running on oeis4.)