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A241969 Number of length 6+3 0..n arrays with no consecutive four elements summing to more than 2*n.

%I A241969 #6 Jul 23 2025 11:15:12
%S A241969 166,4663,53553,365810,1782453,6853011,22111157,62336336,157897575,
%T A241969 366623400,792037896,1610247431,3108255424,5737023770,10183189142,
%U A241969 17463980371,29050569460,47025823517,74283207995,114774423104
%N A241969 Number of length 6+3 0..n arrays with no consecutive four elements summing to more than 2*n.
%C A241969 Row 6 of A241964
%H A241969 R. H. Hardin, <a href="/A241969/b241969.txt">Table of n, a(n) for n = 1..210</a>
%F A241969 Empirical: a(n) = (24187/181440)*n^9 + (57493/40320)*n^8 + (12829/1890)*n^7 + (54583/2880)*n^6 + (296887/8640)*n^5 + (242891/5760)*n^4 + (3196213/90720)*n^3 + (196087/10080)*n^2 + (16343/2520)*n + 1
%e A241969 Some solutions for n=3
%e A241969 ..2....1....2....2....0....0....0....1....3....0....0....2....0....3....0....2
%e A241969 ..0....1....1....1....3....1....2....1....0....1....3....1....2....2....1....2
%e A241969 ..0....3....2....0....1....0....2....2....0....3....0....1....0....0....0....0
%e A241969 ..2....1....0....2....1....3....1....2....1....0....1....2....1....1....0....1
%e A241969 ..3....1....1....0....1....0....0....1....1....2....1....0....0....0....1....0
%e A241969 ..0....0....2....1....1....1....2....0....0....0....3....2....0....2....0....3
%e A241969 ..1....2....1....0....3....1....1....0....0....3....1....1....2....0....0....1
%e A241969 ..2....0....2....2....0....1....0....2....2....0....0....0....0....2....2....1
%e A241969 ..1....2....0....2....0....2....1....3....1....3....2....2....1....0....0....0
%K A241969 nonn
%O A241969 1,1
%A A241969 _R. H. Hardin_, May 03 2014