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%I #7 Oct 31 2018 05:49:35
%S 19,124,486,1421,3437,7280,13980,24897,41767,66748,102466,152061,
%T 219233,308288,424184,572577,759867,993244,1280734,1631245,2054613,
%U 2561648,3164180,3875105,4708431,5679324,6804154,8100541,9587401,11284992
%N Number of length 2+3 0..n arrays with no consecutive four elements summing to more than 2*n.
%H R. H. Hardin, <a href="/A241965/b241965.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (23/60)*n^5 + (9/4)*n^4 + (21/4)*n^3 + (25/4)*n^2 + (58/15)*n + 1.
%F Conjectures from _Colin Barker_, Oct 31 2018: (Start)
%F G.f.: x*(19 + 10*x + 27*x^2 - 15*x^3 + 6*x^4 - x^5) / (1 - x)^6.
%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F (End)
%e Some solutions for n=4:
%e ..2....1....1....1....1....0....0....3....0....1....4....2....4....2....1....4
%e ..0....2....0....2....1....4....0....3....0....0....3....1....0....0....0....4
%e ..2....1....0....3....0....2....2....0....4....3....0....1....2....1....0....0
%e ..1....0....2....1....2....2....2....1....3....2....0....4....0....4....2....0
%e ..1....1....2....2....4....0....4....3....1....0....0....2....0....2....0....3
%Y Row 2 of A241964.
%K nonn
%O 1,1
%A _R. H. Hardin_, May 03 2014
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