A254701 Number of length 3+4 0..n arrays with every five consecutive terms having the maximum of some two terms equal to the minimum of the remaining three terms.

54, 552, 2764, 9507, 25962, 60634, 126456, 242037, 433054, 733788, 1188804, 1854775, 2802450, 4118766, 5909104, 8299689, 11440134, 15506128, 20702268, 27265035, 35465914, 45614658, 58062696, 73206685, 91492206, 113417604

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/5)*n^6 + (19/5)*n^5 + (27/2)*n^4 + (35/2)*n^3 + (123/10)*n^2 + (57/10)*n + 1.

Conjectures from Colin Barker, Dec 17 2018: (Start)

G.f.: x*(54 + 174*x + 34*x^2 - 139*x^3 + 27*x^4 - 7*x^5 + x^6) / (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=7:
..1....4....6....5....6....0....4....4....0....6....1....6....4....5....3....1
..6....6....7....4....5....4....5....1....3....1....6....3....2....2....4....5
..3....4....4....3....3....4....4....4....3....4....0....4....2....2....1....0
..1....4....3....3....3....3....4....4....7....7....1....3....5....0....5....3
..0....6....4....2....0....3....0....7....7....4....3....1....1....2....3....1
..1....1....5....5....7....0....6....4....3....7....1....3....2....4....3....1
..4....7....5....5....3....5....6....0....3....0....6....4....5....2....6....1

Crossrefs

Row 3 of A254698.

Sequence in context: A222968 A228016 A245833 * A086577 A193152 A253006

Adjacent sequences: A254698 A254699 A254700 * A254702 A254703 A254704

Keyword

nonn

Author

R. H. Hardin, Feb 05 2015

Status

approved