A221599 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 1 or less.

128, 1113, 4240, 11011, 22912, 41401, 67936, 103975, 150976, 210397, 283696, 372331, 477760, 601441, 744832, 909391, 1096576, 1307845, 1544656, 1808467, 2100736, 2422921, 2776480, 3162871, 3583552, 4039981, 4533616, 5065915, 5638336

Offset

1,1

Comments

Row 7 of A221596.

Links

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

Formula

Empirical: a(n) = 243*n^3 - 351*n^2 + 237*n + 127 for n>2.

Conjectures from Colin Barker, Aug 09 2018: (Start)

G.f.: x*(128 + 601*x + 556*x^2 + 217*x^3 - 16*x^4 - 28*x^5) / (1 - x)^4.

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

(End)

Example

Some solutions for n=6:
..4....5....5....5....5....2....0....0....1....6....4....3....1....4....5....1
..3....4....6....5....6....2....0....1....1....6....3....2....0....5....4....2
..2....4....5....2....5....1....0....1....4....6....0....1....5....3....3....4
..2....1....3....1....4....5....2....4....5....1....1....1....4....2....4....4
..5....2....2....4....5....4....1....4....3....2....6....0....3....4....2....5
..5....5....1....4....2....4....3....6....3....1....5....3....2....4....3....3
..6....5....1....3....1....5....2....5....4....1....5....4....2....3....4....4

Crossrefs

Cf. A221596.

Sequence in context: A206278 A100628 A344303 * A134630 A133061 A188822

Adjacent sequences: A221596 A221597 A221598 * A221600 A221601 A221602

Keyword

nonn

Author

R. H. Hardin, Jan 20 2013

Status

approved