A268460 Number of length-6 0..n arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.

22, 456, 3146, 13204, 41526, 108032, 245626, 504876, 959414, 1712056, 2901642, 4710596, 7373206, 11184624, 16510586, 23797852, 33585366, 46516136, 63349834, 84976116, 112428662, 146899936, 189756666, 242556044, 307062646, 385266072

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^6 + 6*n^5 + 11*n^4 + 2*n^3 + 6*n - 4.

Conjectures from Colin Barker, Jan 13 2019: (Start)

G.f.: 2*x*(11 + 151*x + 208*x^2 - 6*x^3 - 13*x^4 + 11*x^5 - 2*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=6:
  2  0  2  3  6  4  4  4  3  2  3  6  0  3  1  2
  5  2  6  2  3  2  2  2  2  4  1  0  5  2  5  6
  2  4  4  6  4  4  5  1  2  4  1  4  4  2  0  0
  0  0  0  4  6  1  4  2  4  2  3  0  5  0  3  0
  0  4  3  4  1  0  2  4  4  3  6  5  5  0  5  1
  6  2  0  5  0  1  2  5  6  4  5  6  1  2  2  2

Crossrefs

Row 6 of A268457.

Sequence in context: A014904 A353105 A036905 * A231659 A269681 A269470

Adjacent sequences: A268457 A268458 A268459 * A268461 A268462 A268463

Keyword

nonn

Author

R. H. Hardin, Feb 04 2016

Status

approved