A200843 Number of 0..n arrays x(0..7) of 8 elements without any two consecutive increases or two consecutive decreases.

256, 4057, 28610, 132263, 469116, 1384813, 3570086, 8291391, 17720746, 35389651, 66794740, 120185585, 207567842, 345957699, 558926356, 878476037, 1347291804, 2021416213, 2973396622, 4295957731, 6106254704, 8550764993, 11810879754

Offset

1,1

Comments

Row 6 of A200838.

Links

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

Formula

Empirical: a(n) = (277/4032)*n^8 + (1375/1008)*n^7 + (4933/480)*n^6 + (2723/72)*n^5 + (14161/192)*n^4 + (11197/144)*n^3 + (216211/5040)*n^2 + (929/84)*n + 1.

Conjectures from Colin Barker, Oct 14 2017: (Start)

G.f.: x*(256 + 1753*x + 1313*x^2 - 679*x^3 + 177*x^4 - 77*x^5 + 35*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
..1....1....1....3....0....0....0....0....0....0....0....2....0....3....0....3
..3....1....1....2....3....3....1....1....0....0....2....1....2....2....0....3
..3....0....3....2....2....0....0....1....3....3....2....3....2....2....0....0
..3....1....0....1....3....2....0....3....1....0....0....3....2....1....1....1
..0....0....1....1....3....0....3....0....3....3....2....0....3....1....0....0
..3....3....1....1....2....3....0....2....0....2....0....2....3....3....2....3
..3....2....3....2....2....2....2....1....0....2....2....1....3....1....1....1
..2....3....2....0....0....2....0....3....2....3....1....2....3....3....3....2

Crossrefs

Sequence in context: A231842 A186558 A186554 * A074151 A016804 A115111

Adjacent sequences: A200840 A200841 A200842 * A200844 A200845 A200846

Keyword

nonn

Author

R. H. Hardin Nov 23 2011

Status

approved