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A242147
Number of length 3+5 0..n arrays with no consecutive six elements summing to more than 3*n.
1
132, 2902, 27024, 154647, 647404, 2180310, 6256170, 15876783, 36560854, 77812152, 155155078, 292868433, 527561802, 912752596, 1524615420, 2469089061, 3890540016, 5982195106, 8998569348, 13270128883, 19220442384, 27386087994
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = (757/2240)*n^8 + (14969/5040)*n^7 + (16439/1440)*n^6 + (1133/45)*n^5 + (100771/2880)*n^4 + (22733/720)*n^3 + (92011/5040)*n^2 + (879/140)*n + 1.
Conjectures from Colin Barker, Oct 31 2018: (Start)
G.f.: x*(132 + 1714*x + 5658*x^2 + 4815*x^3 + 1309*x^4 - 30*x^5 + 36*x^6 - 9*x^7 + x^8) / (1 - x)^9.
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.
(End)
EXAMPLE
Some solutions for n=4:
0 1 1 1 2 0 0 0 2 0 2 2 1 2 1 1
2 2 2 3 0 4 2 1 3 2 2 3 2 0 2 1
0 2 0 2 0 0 3 1 0 0 0 1 1 2 0 0
0 0 2 3 1 2 0 0 0 1 4 3 0 1 1 4
4 1 4 0 3 0 0 0 3 1 1 2 4 2 3 2
4 1 0 2 1 4 3 3 3 3 1 0 2 1 2 0
1 4 4 2 4 1 3 0 0 1 1 0 3 1 3 2
0 2 1 1 0 0 1 3 1 0 2 0 1 1 2 1
CROSSREFS
Row 3 of A242144.
Sequence in context: A220925 A220996 A254646 * A023902 A240270 A168180
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 05 2014
STATUS
approved