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

Author

R. H. Hardin Nov 23 2011

Keywords

• nonn

Comments

Row 6 of A200838.

Examples

			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
		

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)