A242145 Number of length 1+5 0..n arrays with no consecutive six elements summing to more than 3*n.

42, 435, 2338, 8688, 25494, 63490, 140148, 282051, 527626, 930237, 1561638, 2515786, 3913014, 5904564, 8677480, 12459861, 17526474, 24204727, 32881002, 44007348, 58108534, 75789462, 97742940, 124757815, 157727466, 197658657

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/2)*n^6 + (131/40)*n^5 + (71/8)*n^4 + (103/8)*n^3 + (85/8)*n^2 + (97/20)*n + 1.

Conjectures from Colin Barker, Oct 31 2018: (Start)

G.f.: x*(42 + 141*x + 175*x^2 - 13*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.

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.

(End)

Example

Some solutions for n=4:
  2  4  2  3  0  2  1  1  0  2  4  0  0  0  1  3
  2  0  1  0  0  4  2  2  0  1  1  3  0  1  2  0
  1  2  1  1  4  2  1  3  1  1  1  0  0  0  3  0
  3  3  4  2  4  1  3  0  1  4  0  0  0  1  3  2
  1  2  3  3  1  1  2  4  0  2  1  2  0  2  1  1
  1  0  0  1  3  2  2  2  4  1  1  3  0  4  2  2

Crossrefs

Row 1 of A242144.

Sequence in context: A027318 A251425 A242144 * A230933 A231110 A156762

Adjacent sequences: A242142 A242143 A242144 * A242146 A242147 A242148

Keyword

nonn

Author

R. H. Hardin, May 05 2014

Status

approved