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A241968 Number of length 5+3 0..n arrays with no consecutive four elements summing to more than 2*n.

%I A241968 #7 Oct 31 2018 06:33:23
%S A241968 97,1895,16649,92037,376559,1247602,3536286,8889273,20314789,42967177,
%T A241968 85231367,160175717,287448747,495702356,825631180,1333724817,
%U A241968 2096836713,3217680571,4831372213,7113141893,10287349127,14637939174,20520487370
%N A241968 Number of length 5+3 0..n arrays with no consecutive four elements summing to more than 2*n.
%H A241968 R. H. Hardin, <a href="/A241968/b241968.txt">Table of n, a(n) for n = 1..210</a>
%F A241968 Empirical: a(n) = (589/3360)*n^8 + (349/210)*n^7 + (2483/360)*n^6 + (1317/80)*n^5 + (35819/1440)*n^4 + (1963/80)*n^3 + (19597/1260)*n^2 + (613/105)*n + 1.
%F A241968 Conjectures from _Colin Barker_, Oct 31 2018: (Start)
%F A241968 G.f.: x*(97 + 1022*x + 3086*x^2 + 2268*x^3 + 632*x^4 - 65*x^5 + 36*x^6 - 9*x^7 + x^8) / (1 - x)^9.
%F A241968 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
%F A241968 (End)
%e A241968 Some solutions for n=4:
%e A241968 ..1....0....1....3....3....1....2....4....0....4....2....4....3....2....1....2
%e A241968 ..2....2....2....0....0....4....2....2....2....2....1....2....0....0....1....3
%e A241968 ..0....0....0....3....2....2....0....0....1....0....0....0....0....0....1....1
%e A241968 ..0....1....4....2....3....1....4....2....4....0....1....2....0....2....1....1
%e A241968 ..2....0....1....1....0....0....1....0....0....4....2....1....3....2....1....3
%e A241968 ..0....4....3....1....3....4....0....2....0....0....0....2....2....0....3....2
%e A241968 ..4....0....0....1....2....2....3....0....2....2....4....0....2....3....3....0
%e A241968 ..2....0....0....3....0....0....3....4....3....2....1....0....1....1....0....3
%Y A241968 Row 5 of A241964.
%K A241968 nonn
%O A241968 1,1
%A A241968 _R. H. Hardin_, May 03 2014