A267475 Number of length-7 0..n arrays with no following elements larger than the first repeated value.

71, 1112, 8770, 44901, 171601, 532840, 1418740, 3357537, 7240267, 14483216, 27233174, 48620533, 83065269, 136640848, 217501096, 336375073, 507134991, 747442216, 1079476394, 1530752741, 2135032537, 2933331864, 3975033628

Offset

1,1

Comments

Row 7 of A267471.

Links

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

Formula

Empirical: a(n) = n^7 + (69/20)*n^6 + (17/2)*n^5 + (97/6)*n^4 + 20*n^3 + (893/60)*n^2 + 6*n + 1.

Conjectures from Colin Barker, Feb 05 2018: (Start)

G.f.: x*(71 + 544*x + 1862*x^2 + 1901*x^3 + 651*x^4 + 4*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=5:
..3....4....0....4....5....2....5....3....2....0....5....5....1....5....0....2
..0....0....4....4....3....0....3....4....0....1....0....0....4....3....2....3
..1....1....1....0....4....4....0....1....5....5....4....2....3....5....0....2
..3....4....2....0....4....2....4....0....5....0....4....4....0....4....3....1
..4....5....3....4....1....0....1....1....4....2....2....0....5....1....5....2
..3....0....3....1....0....4....4....5....2....3....3....1....4....4....2....4
..4....3....3....1....0....2....2....1....2....3....4....4....3....2....1....0

Crossrefs

Cf. A267471.

Sequence in context: A231414 A071827 A289899 * A241940 A254872 A198449

Adjacent sequences: A267472 A267473 A267474 * A267476 A267477 A267478

Keyword

nonn

Author

R. H. Hardin, Jan 15 2016

Status

approved