A268459 Number of length-5 0..n arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.

16, 176, 852, 2776, 7160, 15816, 31276, 56912, 97056, 157120, 243716, 364776, 529672, 749336, 1036380, 1405216, 1872176, 2455632, 3176116, 4056440, 5121816, 6399976, 7921292, 9718896, 11828800, 14290016, 17144676, 20438152, 24219176

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^5 + 5*n^4 + 7*n^3 + n^2 + 2*n.

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

G.f.: 4*x*(4 + 20*x + 9*x^2 - 4*x^3 + x^4) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

Some solutions for n=9:
  7  5  8  9  3  4  1  2  0  4  3  1  5  1  5  3
  1  4  0  0  3  4  6  4  1  4  6  5  9  8  7  0
  3  1  2  5  2  7  1  2  3  7  4  6  7  6  6  3
  6  1  7  6  1  6  7  1  6  5  4  8  6  6  5  9
  1  1  9  6  5  3  5  8  3  6  4  9  4  6  5  7

Crossrefs

Row 5 of A268457.

Sequence in context: A017931 A021129 A268869 * A070030 A283278 A231127

Adjacent sequences: A268456 A268457 A268458 * A268460 A268461 A268462

Keyword

nonn

Author

R. H. Hardin, Feb 04 2016

Status

approved