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A220564 Number of ways to reciprocally link elements of an 3 X n array either to themselves or to exactly one horizontal or antidiagonal neighbor. 1

%I #7 Aug 01 2018 04:56:24

%S 1,13,64,430,2604,16310,101052,628269,3901815,24240377,150578968,

%T 935414825,5810847665,36097422853,224239670624,1392992694942,

%U 8653368270212,53755331997318,333931897912068,2074408410086741

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

%C Row 3 of A220562.

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

%F 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).

%F 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

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

%e ..0..6..4....6..4..0....0..7..0....0..7..7....0..6..4....6..4..7....0..0..0

%e ..6..4..0....0..7..0....3..0..0....3..3..7....0..0..0....0..3..7....6..4..0

%e ..0..6..4....3..0..0....6..4..0....0..3..0....0..0..0....0..3..0....0..6..4

%Y Cf. A220562.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 16 2012

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Last modified February 21 16:55 EST 2024. Contains 370237 sequences. (Running on oeis4.)