A221686 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 1 or less, starting with 0.

64, 320, 844, 1692, 2856, 4326, 6102, 8184, 10572, 13266, 16266, 19572, 23184, 27102, 31326, 35856, 40692, 45834, 51282, 57036, 63096, 69462, 76134, 83112, 90396, 97986, 105882, 114084, 122592, 131406, 140526, 149952, 159684, 169722, 180066, 190716

Offset

1,1

Comments

Row 7 of A221683.

Links

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

Formula

Empirical: a(n) = 153*n^2 - 213*n + 96 for n>3.

Conjectures from Colin Barker, Aug 10 2018: (Start)

G.f.: 2*x*(32 + 64*x + 38*x^2 + 28*x^3 - 4*x^4 - 5*x^5) / (1 - x)^3.

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

(End)

Example

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

Crossrefs

Cf. A221683.

Sequence in context: A251196 A221486 A231942 * A211258 A252080 A017366

Adjacent sequences: A221683 A221684 A221685 * A221687 A221688 A221689

Keyword

nonn

Author

R. H. Hardin, Jan 22 2013

Status

approved