A249962 Number of length 2+5 0..n arrays with no six consecutive terms having the maximum of any two terms equal to the minimum of the remaining four terms.

15, 505, 5300, 31180, 129095, 422065, 1164800, 2830080, 6226935, 12655665, 24104740, 43494620, 74973535, 124270265, 199108960, 309691040, 469249215, 694678665, 1007250420, 1433411980, 2005680215, 2763631585, 3754994720

Offset

1,1

Comments

Row 2 of A249960.

Links

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

Formula

Empirical: a(n) = n^7 + (13/6)*n^6 + (13/3)*n^5 + (65/12)*n^4 + (3/2)*n^3 - (1/12)*n^2 + (2/3)*n.

Conjectures from Colin Barker, Aug 21 2017: (Start)

G.f.: 5*x*(1 + x)*(3 + 74*x + 262*x^2 + 154*x^3 + 11*x^4) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

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

Crossrefs

Sequence in context: A208099 A219057 A203525 * A004703 A218188 A218365

Adjacent sequences: A249959 A249960 A249961 * A249963 A249964 A249965

Keyword

nonn

Author

R. H. Hardin, Nov 09 2014

Status

approved