A250017 Number of length 3+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, 912, 13512, 106352, 558588, 2224848, 7259024, 20384352, 50937444, 115954256, 244606296, 484335696, 909078092, 1630002576, 2809238304, 4677097664, 7553346228, 11873110032, 18218051048, 27353482032, 40272132252, 58245315920

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^8 + (41/35)*n^7 + (56/15)*n^6 + (22/5)*n^5 + (19/3)*n^4 + (17/5)*n^3 - (16/15)*n^2 + (36/35)*n.

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

G.f.: 4*x*(5 + 183*x + 1506*x^2 + 3974*x^3 + 3441*x^4 + 903*x^5 + 68*x^6) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8.

(End)

Example

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

Crossrefs

Row 3 of A250014.

Sequence in context: A192370 A113102 A285673 * A305116 A066802 A354814

Adjacent sequences: A250014 A250015 A250016 * A250018 A250019 A250020

Keyword

nonn

Author

R. H. Hardin, Nov 10 2014

Status

approved