A249845 Number of length 1+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, 110, 560, 1920, 5170, 11830, 24080, 44880, 78090, 128590, 202400, 306800, 450450, 643510, 897760, 1226720, 1645770, 2172270, 2825680, 3627680, 4602290, 5775990, 7177840, 8839600, 10795850, 13084110, 15744960, 18822160, 22362770

Offset

1,1

Comments

Row 1 of A249844.

Links

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

Formula

Empirical: a(n) = n^5 + (5/2)*n^4 + (10/3)*n^3 + (5/2)*n^2 + (2/3)*n.

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

G.f.: 10*x*(1 + x)*(1 + 4*x + x^2) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Sequence in context: A043996 A044723 A158492 * A180290 A110251 A270243

Adjacent sequences: A249842 A249843 A249844 * A249846 A249847 A249848

Keyword

nonn

Author

R. H. Hardin, Nov 07 2014

Status

approved