A250015 Number of length 1+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, 300, 2040, 8840, 28860, 77700, 182000, 383760, 745380, 1355420, 2335080, 3845400, 6095180, 9349620, 13939680, 20272160, 28840500, 40236300, 55161560, 74441640, 99038940, 130067300, 168807120, 216721200, 275471300, 346935420

Offset

1,1

Links

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

Formula

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

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

G.f.: 20*x*(1 + 4*x + x^2)^2 / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Row 1 of A250014.

Sequence in context: A322052 A250014 A291256 * A344197 A138794 A077758

Adjacent sequences: A250012 A250013 A250014 * A250016 A250017 A250018

Keyword

nonn

Author

R. H. Hardin, Nov 10 2014

Status

approved