A200787 Number of 0..n arrays x(0..4) of 5 elements without any two consecutive increases.

32, 216, 840, 2425, 5796, 12152, 23136, 40905, 68200, 108416, 165672, 244881, 351820, 493200, 676736, 911217, 1206576, 1573960, 2025800, 2575881, 3239412, 4033096, 4975200, 6085625, 7385976, 8899632, 10651816, 12669665, 14982300

Offset

1,1

Comments

Row 3 of A200785.

Links

R. H. Hardin, Table of n, a(n) for n = 1..139

Formula

Empirical: a(n) = (7/12)*n^5 + (47/12)*n^4 + (39/4)*n^3 + (133/12)*n^2 + (17/3)*n + 1.

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

G.f.: x*(32 + 24*x + 24*x^2 - 15*x^3 + 6*x^4 - x^5) / (1 - x)^6.

a(n) = (1 + n)^2*(12 + 44*n + 33*n^2 + 7*n^3) / 12 .

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Sequence in context: A125342 A126500 A160538 * A250354 A146089 A250232

Adjacent sequences: A200784 A200785 A200786 * A200788 A200789 A200790

Keyword

nonn

Author

R. H. Hardin, Nov 22 2011

Status

approved