A250062 Number of length 3+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, 2292, 50028, 505154, 3213429, 15002490, 56118016, 177725772, 494492733, 1240508808, 2859421884, 6142632990, 12432735341, 23913080862, 44008420512, 77925990328, 133371203589, 221477260860, 357993503916, 564783216666

Offset

1,1

Comments

Row 3 of A250059.

Links

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

Formula

Empirical: a(n) = n^9 + (37/21)*n^8 + (39/7)*n^7 + (17/2)*n^6 + (13/15)*n^5 + (17/12)*n^4 + (10/3)*n^3 - (33/28)*n^2 - (19/70)*n.

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

G.f.: x*(21 + 2082*x + 28053*x^2 + 105494*x^3 + 142519*x^4 + 72798*x^5 + 11647*x^6 + 266*x^7) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)

Example

Some solutions for n=3:
..1....2....0....2....3....2....3....0....2....2....3....1....1....1....2....0
..3....3....0....2....2....3....3....3....3....2....0....2....2....3....2....3
..2....0....2....3....2....3....0....0....2....3....3....0....3....0....1....3
..3....2....2....0....1....1....3....2....0....3....0....1....0....1....2....3
..0....2....2....1....0....2....3....2....0....2....2....1....0....0....0....0
..2....0....2....3....3....2....3....1....3....1....1....0....1....1....3....1
..0....1....1....0....0....0....1....3....2....1....2....3....3....2....0....1
..3....2....2....1....3....3....3....0....1....2....3....2....2....1....2....0
..1....3....0....2....3....3....3....3....2....3....0....2....2....1....1....3

Crossrefs

Sequence in context: A319170 A359223 A215160 * A219000 A033510 A123844

Adjacent sequences: A250059 A250060 A250061 * A250063 A250064 A250065

Keyword

nonn

Author

R. H. Hardin, Nov 11 2014

Status

approved