A250016 Number of length 2+5 0..n arrays with no six consecutive terms having the maximum of any three terms equal to the minimum of the remaining three terms.

20, 520, 5200, 30360, 125780, 412160, 1140160, 2776080, 6119220, 12455960, 23755600, 42913000, 74043060, 122832080, 196951040, 306535840, 464739540, 688361640, 998559440, 1421646520, 1989983380, 2742965280, 3728112320

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^7 + 2*n^6 + 4*n^5 + 5*n^4 + (17/3)*n^3 + 3*n^2 - (2/3)*n.

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

G.f.: 20*x*(1 + 4*x + x^2)*(1 + 14*x + 23*x^2 + 4*x^3) / (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:
..2....2....1....2....5....0....2....2....1....1....1....5....0....3....1....1
..3....4....2....0....1....1....0....4....1....1....5....0....5....2....2....3
..0....4....5....2....2....3....4....5....1....3....3....5....1....2....5....2
..0....5....3....5....4....4....0....0....3....2....0....2....2....5....3....0
..0....1....4....5....1....5....4....5....4....0....4....1....5....4....4....4
..1....1....2....3....4....5....5....0....5....4....1....5....3....1....1....5
..3....3....0....2....3....1....1....0....4....0....5....0....0....4....2....1

Crossrefs

Row 2 of A250014.

Sequence in context: A008270 A130186 A130033 * A371017 A337352 A180882

Adjacent sequences: A250013 A250014 A250015 * A250017 A250018 A250019

Keyword

nonn

Author

R. H. Hardin, Nov 10 2014

Status

approved