A250060 Number of length 1+6 0..n arrays with no seven consecutive terms having the maximum of any two terms equal to the minimum of the remaining five terms.

21, 735, 7224, 40320, 160545, 509691, 1375080, 3281544, 7116165, 14290815, 26947536, 48211800, 82498689, 135877035, 216496560, 335083056, 505506645, 745428159, 1077028680, 1527827280, 2131592001, 2929349115, 3970495704

Offset

1,1

Comments

Row 1 of A250059.

Links

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

Formula

Empirical: a(n) = n^7 + (7/2)*n^6 + 7*n^5 + (35/4)*n^4 + (7/2)*n^3 - (7/4)*n^2 - n.

Conjectures from Colin Barker, Aug 22 2017: (Start)

G.f.: 21*x*(1 + x)*(1 + 26*x + 66*x^2 + 26*x^3 + x^4) / (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:
..4....2....1....2....0....2....4....2....1....2....1....1....2....2....1....1
..1....0....5....4....3....3....0....5....4....1....2....1....5....2....5....0
..2....4....5....3....4....3....3....0....3....5....2....3....4....2....4....0
..0....4....0....3....0....0....3....2....4....2....1....5....0....1....1....2
..2....1....0....0....5....1....3....2....2....0....4....4....1....1....2....2
..2....4....2....5....1....0....3....0....2....0....4....3....4....2....3....3
..3....0....2....0....1....4....1....1....1....5....4....5....0....3....5....5

Crossrefs

Sequence in context: A317824 A297504 A250059 * A078791 A201069 A143002

Adjacent sequences: A250057 A250058 A250059 * A250061 A250062 A250063

Keyword

nonn

Author

R. H. Hardin, Nov 11 2014

Status

approved