A250084 Number of length 3+5 0..n arrays with every six consecutive terms having the maximum of some two terms equal to the minimum of the remaining four terms.

144, 2228, 15472, 68863, 232096, 647122, 1572320, 3441309, 6938416, 13092816, 23393360, 39926107, 65536576, 104018734, 160332736, 240853433, 353651664, 508810348, 718777392, 998757431, 1367144416, 1845997066, 2461559200

Offset

1,1

Links

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

Formula

Empirical: a(n) = (2/5)*n^7 + (19/3)*n^6 + (47/2)*n^5 + 37*n^4 + (183/5)*n^3 + (83/3)*n^2 + (23/2)*n + 1.

Conjectures from Colin Barker, Nov 11 2018: (Start)

G.f.: x*(144 + 1076*x + 1680*x^2 - 593*x^3 - 280*x^4 - 18*x^5 + 8*x^6 - x^7) / (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=4:
..0....2....4....2....2....2....3....3....4....3....2....4....3....1....3....0
..2....4....2....4....0....3....2....2....0....3....3....1....1....1....1....1
..0....4....1....0....0....0....4....0....0....3....2....4....1....1....1....0
..3....0....4....0....1....1....4....2....1....0....2....2....2....1....4....1
..0....0....1....0....0....1....0....4....0....4....1....2....3....1....4....0
..0....0....1....3....4....2....2....2....4....3....4....2....0....3....0....4
..0....0....3....0....1....2....3....4....3....3....3....2....1....3....1....0
..3....4....1....2....0....2....2....2....0....4....4....2....4....0....2....0

Crossrefs

Row 3 of A250081.

Sequence in context: A368508 A066445 A008431 * A280025 A223687 A268625

Adjacent sequences: A250081 A250082 A250083 * A250085 A250086 A250087

Keyword

nonn

Author

R. H. Hardin, Nov 11 2014

Status

approved