A200790 Number of 0..n arrays x(0..7) of 8 elements without any two consecutive increases.

256, 5157, 43681, 232275, 919413, 2964416, 8216484, 20273247, 45611500, 95196145, 186686721, 347374261, 617994573, 1057577400, 1749504272, 2808961221, 4391985888, 6706321909, 10024306825, 14698033119, 21177035341, 30028769640

Offset

1,1

Comments

Row 6 of A200785.

Links

R. H. Hardin, Table of n, a(n) for n = 1..136

Formula

Empirical: a(n) = (6679/20160)*n^8 + (4799/1260)*n^7 + (26449/1440)*n^6 + (2162/45)*n^5 + (212153/2880)*n^4 + (6019/90)*n^3 + (174571/5040)*n^2 + (3893/420)*n + 1.

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

G.f.: x*(256 + 2853*x + 6484*x^2 + 3294*x^3 + 522*x^4 - 79*x^5 + 36*x^6 - 9*x^7 + x^8) / (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>9.

(End)

Example

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

Crossrefs

Sequence in context: A074151 A016804 A115111 * A206110 A196152 A113173

Adjacent sequences: A200787 A200788 A200789 * A200791 A200792 A200793

Keyword

nonn

Author

R. H. Hardin, Nov 22 2011

Status

approved