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A242146 Number of length 2+5 0..n arrays with no consecutive six elements summing to more than 3*n.

%I A242146 #8 Oct 31 2018 18:42:23
%S A242146 74,1113,7862,36224,126894,367358,924300,2088459,4333978,8394287,
%T A242146 15356562,26776802,44817566,72410412,113445080,172987461,257528394,
%U A242146 375265333,536418926,753586548,1042134830,1420633226,1911330660
%N A242146 Number of length 2+5 0..n arrays with no consecutive six elements summing to more than 3*n.
%H A242146 R. H. Hardin, <a href="/A242146/b242146.txt">Table of n, a(n) for n = 1..210</a>
%F A242146 Empirical: a(n) = (1021/2520)*n^7 + (28/9)*n^6 + (3679/360)*n^5 + (1349/72)*n^4 + (1873/90)*n^3 + (1019/72)*n^2 + (779/140)*n + 1.
%F A242146 Conjectures from _Colin Barker_, Oct 31 2018: (Start)
%F A242146 G.f.: x*(74 + 521*x + 1030*x^2 + 348*x^3 + 90*x^4 - 28*x^5 + 8*x^6 - x^7) / (1 - x)^8.
%F A242146 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F A242146 (End)
%e A242146 Some solutions for n=4:
%e A242146 ..2....1....4....0....2....3....1....0....3....0....1....4....0....1....0....3
%e A242146 ..1....1....2....2....4....0....1....2....0....3....3....3....3....1....0....4
%e A242146 ..0....3....3....1....0....2....0....3....4....4....3....2....1....3....4....0
%e A242146 ..0....2....3....1....4....3....2....0....0....1....0....1....2....1....1....2
%e A242146 ..0....1....0....3....1....0....4....1....3....1....0....2....0....0....0....3
%e A242146 ..1....2....0....2....0....3....1....2....0....0....0....0....0....0....1....0
%e A242146 ..1....0....3....2....2....1....0....2....4....0....4....1....2....2....4....1
%Y A242146 Row 2 of A242144.
%K A242146 nonn
%O A242146 1,1
%A A242146 _R. H. Hardin_, May 05 2014