A200791 Number of 0..n arrays x(0..8) of 9 elements without any two consecutive increases.

512, 14849, 163020, 1062500, 4975322, 18514405, 58154912, 160338680, 398601390, 910893148, 1941103528, 3899741885, 7449762880, 13624665670, 23987233104, 40838614531, 67488892468, 108601809395, 170627966340, 262342539690

Offset

1,1

Comments

Row 7 of A200785.

Links

R. H. Hardin, Table of n, a(n) for n = 1..135

Formula

Empirical: a(n) = (99377/362880)*n^9 + (48247/13440)*n^8 + (243673/12096)*n^7 + (60529/960)*n^6 + (2076437/17280)*n^5 + (274529/1920)*n^4 + (952027/9072)*n^3 + (152461/3360)*n^2 + (26399/2520)*n + 1.

Conjectures from Colin Barker, Oct 15 2017: (Start)

G.f.: x*(512 + 9729*x + 37570*x^2 + 39065*x^3 + 11862*x^4 + 551*x^5 + 124*x^6 - 45*x^7 + 10*x^8 - x^9) / (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
..0....0....0....0....0....1....1....1....3....0....1....0....1....1....3....1
..0....0....0....3....3....3....3....3....0....3....3....3....0....1....1....3
..3....0....2....0....1....0....0....1....0....2....3....3....2....2....0....1
..2....1....0....3....0....3....0....3....1....2....1....3....1....2....1....0
..2....1....3....3....0....0....2....3....0....3....1....1....0....3....1....0
..3....3....2....0....3....0....0....1....2....3....3....0....3....2....3....2
..2....2....2....3....2....2....0....1....1....1....2....1....1....0....1....1
..1....3....3....2....3....0....0....3....1....0....2....1....0....1....0....0
..3....0....1....2....3....1....3....2....3....2....2....0....0....0....3....2

Crossrefs

Sequence in context: A256947 A254720 A254252 * A254812 A329894 A258523

Adjacent sequences: A200788 A200789 A200790 * A200792 A200793 A200794

Keyword

nonn

Author

R. H. Hardin, Nov 22 2011

Status

approved