A202730 Number of n X 3 nonnegative integer arrays each row and column an ascent sequence (interior element no greater than one plus up-steps preceding it) and the lower right element equal to min(n,3)-1.

1, 2, 2, 14, 78, 406, 2062, 10374, 51998, 260246, 1301742, 6509734, 32550718, 162757686, 813796622, 4068999494, 20345030238, 101725216726, 508626214702, 2543131335654, 12715657202558, 63578287061366, 317891437403982

Offset

1,2

Comments

Column 3 of A202735.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) -10*a(n-2) for n>4.

Conjectures from Colin Barker, Jun 01 2018: (Start)

G.f.: x*(1 - 5*x - 2*x^2 + 20*x^3) / ((1 - 2*x)*(1 - 5*x)).

a(n) = (4*5^n - 25*2^n)/150 for n>2.

(End)

Example

Some solutions for n=4:
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..0..0..1....0..1..1....0..1..1....0..0..0....0..0..1....0..1..0....0..0..1
..0..1..2....0..1..2....0..1..0....0..0..1....0..1..0....0..1..1....0..0..0
..0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2

Crossrefs

Cf. A202735.

Sequence in context: A345370 A166114 A366364 * A292080 A333372 A350923

Adjacent sequences: A202727 A202728 A202729 * A202731 A202732 A202733

Keyword

nonn

Author

R. H. Hardin, Dec 23 2011

Status

approved