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%I #8 Feb 22 2018 16:29:08
%S 1,4,34,500,10867,313132,10856948,418689772,17067989413,715189507700,
%T 30371156968582,1298083132473604,55654030558406039,
%U 2389712969490386908,102686352402421016536,4414019789796312628796,189771542890022982723145
%N Number of n X 2 0..7 arrays with values 0..7 introduced in row major order and no element equal to any horizontal or vertical neighbor.
%C Column 2 of A198914.
%H R. H. Hardin, <a href="/A198908/b198908.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 88*a(n-1) - 2613*a(n-2) + 33232*a(n-3) - 184531*a(n-4) + 400344*a(n-5) - 246519*a(n-6).
%F Conjectures from _Colin Barker_, Feb 22 2018: (Start)
%F G.f.: x*(1 - 84*x + 2295*x^2 - 25272*x^3 + 107312*x^4 - 128772*x^5) / ((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 13*x)*(1 - 21*x)*(1 - 43*x)).
%F a(n) = (1036945 + 344344*3^n + 75465*7^n + 12040*13^n + 2795*21^n + 91*43^n) / 2817360.
%F (End)
%e Some solutions with values 0 to 7 for n=5:
%e ..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
%e ..2..3....2..3....1..2....2..3....2..3....2..3....2..3....2..3....2..3....2..3
%e ..4..5....4..2....3..4....4..5....4..5....4..5....4..5....4..5....4..5....4..5
%e ..0..3....1..5....5..6....2..3....6..7....3..6....6..2....6..1....0..6....6..7
%e ..6..7....6..7....2..7....6..7....7..1....7..3....2..7....5..7....7..1....2..4
%Y Cf. A198914.
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 31 2011
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