A250339 Number of length 3+5 0..n arrays with every six consecutive terms having the maximum of some three terms equal to the minimum of the remaining three terms.

108, 1989, 14040, 62041, 206724, 569693, 1369136, 2966769, 5927452, 11092917, 19671048, 33342153, 54383668, 85814733, 131562080, 196648673, 287406540, 411715237, 579267384, 801862713, 1093732068, 1471892797, 1956536976

Offset

1,1

Links

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

Formula

Empirical: a(n) = (2/7)*n^7 + (28/5)*n^6 + (112/5)*n^5 + (109/3)*n^4 + (94/3)*n^3 + (166/15)*n^2 - (2/105)*n + 1.

Conjectures from Colin Barker, Nov 12 2018: (Start)

G.f.: x*(108 + 1125*x + 1152*x^2 - 635*x^3 - 308*x^4 - 9*x^5 + 8*x^6 - x^7) / (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=4:
..3....2....0....2....2....0....0....1....4....3....4....4....3....2....0....3
..1....3....3....0....1....4....3....4....2....2....0....1....2....1....2....3
..3....0....2....2....0....0....3....0....0....4....3....2....4....1....1....0
..3....4....2....3....1....3....3....1....2....3....1....2....3....0....1....3
..4....2....1....0....1....3....3....1....0....0....3....3....3....1....0....3
..3....2....3....2....4....3....1....1....2....3....3....2....3....1....4....3
..0....0....0....2....0....3....3....4....2....3....4....0....2....3....0....3
..1....2....4....2....4....4....3....1....2....4....3....0....3....3....4....0

Crossrefs

Row 3 of A250336.

Sequence in context: A279981 A233317 A263970 * A263961 A202427 A063809

Adjacent sequences: A250336 A250337 A250338 * A250340 A250341 A250342

Keyword

nonn

Author

R. H. Hardin, Nov 19 2014

Status

approved