A221597 Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 1 or less.

32, 139, 342, 651, 1068, 1593, 2226, 2967, 3816, 4773, 5838, 7011, 8292, 9681, 11178, 12783, 14496, 16317, 18246, 20283, 22428, 24681, 27042, 29511, 32088, 34773, 37566, 40467, 43476, 46593, 49818, 53151, 56592, 60141, 63798, 67563, 71436, 75417, 79506

Offset

1,1

Comments

Row 5 of A221596.

Links

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

Formula

Empirical: a(n) = 54*n^2 - 69*n + 63 for n>2.

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

G.f.: x*(32 + 43*x + 21*x^2 + 10*x^3 + 2*x^4) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.

(End)

Example

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

Crossrefs

Cf. A221596.

Sequence in context: A299185 A299946 A137740 * A159763 A100164 A048191

Adjacent sequences: A221594 A221595 A221596 * A221598 A221599 A221600

Keyword

nonn

Author

R. H. Hardin, Jan 20 2013

Status

approved