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

Row 3 of A220562.

Empirical: a(n) = 4*a(n-1) + 15*a(n-2) - 5*a(n-3) - 19*a(n-4) + 9*a(n-5) + 2*a(n-6) - a(n-7).

Empirical g.f.: x*(1 - x)*(1 + 10*x + 7*x^2 - 9*x^3 - x^4 + x^5) / ((1 + x - x^2)*(1 - 5*x - 9*x^2 + 9*x^3 + x^4 - x^5)). - Colin Barker, Aug 01 2018

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

Cf. A220562.

R. H. Hardin , Dec 16 2012

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R. H. Hardin, <a href="/A220564/b220564.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of ways to reciprocally link elements of an 3Xn array either to themselves or to exactly one horizontal or antidiagonal neighbor

1, 13, 64, 430, 2604, 16310, 101052, 628269, 3901815, 24240377, 150578968, 935414825, 5810847665, 36097422853, 224239670624, 1392992694942, 8653368270212, 53755331997318, 333931897912068, 2074408410086741

1,2

Row 3 of A220562

Empirical: a(n) = 4*a(n-1) +15*a(n-2) -5*a(n-3) -19*a(n-4) +9*a(n-5) +2*a(n-6) -a(n-7)

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

..0..6..4....6..4..0....0..7..0....0..7..7....0..6..4....6..4..7....0..0..0

..6..4..0....0..7..0....3..0..0....3..3..7....0..0..0....0..3..7....6..4..0

..0..6..4....3..0..0....6..4..0....0..3..0....0..0..0....0..3..0....0..6..4

allocated

nonn

R. H. Hardin Dec 16 2012

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allocated for R. H. Hardin

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