A200842 Number of 0..n arrays x(0..6) of 7 elements without any two consecutive increases or two consecutive decreases.

128, 1465, 8210, 31677, 96690, 250913, 577660, 1212729, 2365804, 4346969, 7598878, 12735125, 20585358, 32247681, 49148888, 73113073, 106439160, 151987897, 213278858, 294597997, 401116298, 539020065, 715653396, 939673385, 1221218596

Offset

1,1

Comments

Row 5 of A200838.

Links

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

Formula

Empirical: a(n) = (34/315)*n^7 + (163/90)*n^6 + (1981/180)*n^5 + (557/18)*n^4 + (7807/180)*n^3 + (1361/45)*n^2 + (333/35)*n + 1.

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

G.f.: x*(128 + 441*x + 74*x^2 - 151*x^3 + 74*x^4 - 29*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=3
..3....2....2....0....0....2....1....2....3....1....2....0....2....3....3....0
..1....1....2....1....1....1....0....0....3....1....0....3....0....3....0....2
..1....1....0....1....1....2....3....1....0....0....0....2....0....3....2....1
..1....2....0....0....1....0....0....0....2....1....3....2....0....2....0....2
..3....1....3....0....1....0....2....3....1....0....2....1....3....2....1....2
..1....1....3....0....3....3....1....3....2....0....3....3....1....0....1....2
..1....0....3....3....2....0....1....1....2....2....2....1....1....2....3....3

Crossrefs

Sequence in context: A221071 A070055 A247930 * A187706 A202961 A239540

Adjacent sequences: A200839 A200840 A200841 * A200843 A200844 A200845

Keyword

nonn

Author

R. H. Hardin Nov 23 2011

Status

approved