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%I #8 Jul 31 2018 18:40:09
%S 3,29,224,1814,14556,117022,940432,7558245,60744605,488197825,
%T 3923590632,31533457665,253430854415,2036795298237,16369494914388,
%U 131559791031398,1057331255850916,8497652480629342,68294678022457540,548876652325439237
%N Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.
%C Column 3 of A220553.
%H R. H. Hardin, <a href="/A220548/b220548.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) + 17*a(n-2) - 3*a(n-3) - 17*a(n-4) + 3*a(n-5) + 4*a(n-6) - a(n-7).
%F Empirical g.f.: x*(3 + 11*x - x^2 - 14*x^3 + 2*x^4 + 4*x^5 - x^6) / ((1 + x - x^2)*(1 - 7*x - 9*x^2 + 5*x^3 + 3*x^4 - x^5)). - _Colin Barker_, Jul 31 2018
%e Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10):
%e ..0..7..7....0..0..0....0..8..8....8..0..0....8..6..4....6..4..7....0..0..7
%e ..3..3..0....8..6..4....8..2..2....2..0..8....2..6..4....0..3..7....8..3..7
%e ..0..0..0....2..6..4....2..0..0....6..4..2....0..6..4....0..3..0....2..3..0
%Y Cf. A220553.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 15 2012
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