A250388 Number of length 2+3 0..n arrays with no four consecutive terms having the maximum of any two terms equal to the minimum of the remaining two terms.

6, 78, 432, 1560, 4350, 10206, 21168, 40032, 70470, 117150, 185856, 283608, 418782, 601230, 842400, 1155456, 1555398, 2059182, 2685840, 3456600, 4395006, 5527038, 6881232, 8488800, 10383750, 12603006, 15186528, 18177432, 21622110, 25570350

Offset

1,1

Comments

Row 2 of A250387.

Links

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

Formula

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

Conjectures from Colin Barker, Aug 20 2017: (Start)

G.f.: 6*x*(1 + x)*(1 + 6*x + 3*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....4....1....3....2....1....1....6....6....1....5....1....0....2....6....4
..3....6....2....0....5....2....0....6....4....5....6....0....5....2....2....6
..1....2....3....5....6....6....6....1....1....0....6....6....5....5....4....5
..1....0....4....5....0....5....6....2....0....6....0....4....1....4....3....1
..5....1....5....0....1....0....5....6....0....3....3....3....4....5....1....0

Crossrefs

Sequence in context: A116280 A134788 A167498 * A231248 A160240 A069669

Adjacent sequences: A250385 A250386 A250387 * A250389 A250390 A250391

Keyword

nonn

Author

R. H. Hardin, Nov 20 2014

Status

approved