A249847 Number of length 3+4 0..n arrays with no five consecutive terms having the maximum of any two terms equal to the minimum of the remaining three terms.

10, 359, 4064, 25206, 108250, 363349, 1022672, 2522796, 5618202, 11530915, 22141328, 40225250, 69742218, 116180113, 186961120, 291914072, 443818218, 659023455, 958152064, 1366886990, 1916851706, 2646586701, 3602627632

Offset

1,1

Comments

Row 3 of A249844.

Links

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

Formula

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

Conjectures from Colin Barker, Aug 18 2017: (Start)

G.f.: x*(10 + 279*x + 1472*x^2 + 2186*x^3 + 990*x^4 + 103*x^5) / (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
..0....1....4....3....1....0....5....1....1....5....5....0....5....4....2....5
..4....5....0....2....4....0....0....2....2....1....3....0....2....4....3....2
..5....1....3....0....0....2....5....4....3....0....0....3....4....0....0....1
..3....4....2....0....0....1....2....1....0....4....4....3....1....0....3....5
..2....2....3....3....2....4....4....4....2....0....2....2....3....2....1....4
..1....1....0....5....4....0....0....5....1....2....0....3....4....2....4....0
..1....2....0....4....2....5....0....3....5....4....5....0....2....3....4....0

Crossrefs

Sequence in context: A217508 A217509 A016101 * A185255 A160523 A301310

Adjacent sequences: A249844 A249845 A249846 * A249848 A249849 A249850

Keyword

nonn

Author

R. H. Hardin, Nov 07 2014

Status

approved