A242147 Number of length 3+5 0..n arrays with no consecutive six elements summing to more than 3*n.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

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

Adjacent sequences: A242144 A242145 A242146 * A242148 A242149 A242150

Keyword

nonn

Author

R. H. Hardin, May 05 2014

Status

approved