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A241966 Number of length 3+3 0..n arrays with no consecutive four elements summing to more than 2*n.

%I A241966 #8 Oct 31 2018 06:33:43
%S A241966 33,311,1597,5778,16660,40978,89622,179079,333091,584529,977483,
%T A241966 1569568,2434446,3664564,5374108,7702173,10816149,14915323,20234697,
%U A241966 27049022,35677048,46485990,59896210,76386115,96497271,120839733,150097591
%N A241966 Number of length 3+3 0..n arrays with no consecutive four elements summing to more than 2*n.
%H A241966 R. H. Hardin, <a href="/A241966/b241966.txt">Table of n, a(n) for n = 1..210</a>
%F A241966 Empirical: a(n) = (3/10)*n^6 + (127/60)*n^5 + (149/24)*n^4 + (59/6)*n^3 + (1079/120)*n^2 + (91/20)*n + 1.
%F A241966 Conjectures from _Colin Barker_, Oct 31 2018: (Start)
%F A241966 G.f.: x*(33 + 80*x + 113*x^2 - 25*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.
%F A241966 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A241966 (End)
%e A241966 Some solutions for n=4:
%e A241966 ..4....1....0....3....2....1....4....1....1....2....3....0....4....3....2....0
%e A241966 ..3....0....4....4....0....1....0....4....0....4....2....4....3....1....0....3
%e A241966 ..1....0....0....0....0....1....0....1....0....0....2....0....1....3....2....4
%e A241966 ..0....1....0....1....3....0....0....0....2....0....1....3....0....1....0....1
%e A241966 ..4....4....0....3....1....3....1....3....3....0....0....0....3....1....4....0
%e A241966 ..1....2....0....3....1....0....0....2....2....4....2....3....2....0....1....3
%Y A241966 Row 3 of A241964.
%K A241966 nonn
%O A241966 1,1
%A A241966 _R. H. Hardin_, May 03 2014