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Number of length 2+4 0..n arrays with no consecutive five elements summing to more than 2*n.
1

%I #8 Oct 30 2018 20:20:23

%S 26,218,1043,3599,10031,24052,51570,101421,186208,323246,535613,

%T 853307,1314509,1966952,2869396,4093209,5724054,7863682,10631831,

%U 14168231,18634715,24217436,31129190,39611845,49938876,62418006,77393953,95251283

%N Number of length 2+4 0..n arrays with no consecutive five elements summing to more than 2*n.

%H R. H. Hardin, <a href="/A241938/b241938.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (53/360)*n^6 + (5/4)*n^5 + (307/72)*n^4 + (91/12)*n^3 + (683/90)*n^2 + (25/6)*n + 1.

%F Conjectures from _Colin Barker_, Oct 30 2018: (Start)

%F G.f.: x*(26 + 36*x + 63*x^2 - 34*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.

%F 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 (End)

%e Some solutions for n=4:

%e ..3....1....1....0....1....2....2....1....0....1....2....0....2....1....3....2

%e ..1....3....1....1....2....0....1....0....3....0....1....0....1....3....0....2

%e ..2....1....1....1....2....1....0....2....1....0....2....2....2....2....1....1

%e ..0....2....0....3....1....4....3....1....1....4....0....0....3....1....1....0

%e ..1....1....0....3....0....0....1....0....1....0....3....1....0....1....0....0

%e ..4....1....1....0....0....1....0....2....2....1....0....4....0....1....0....1

%Y Row 2 of A241936.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 02 2014