A222993 Number of n X 2 0..2 arrays with successive rows and columns fitting to straight lines with nondecreasing slope, with a single point array taken as having zero slope.

9, 50, 222, 867, 3123, 10660, 35064, 112373, 353517, 1097430, 3374226, 10302919, 31301991, 94757960, 286108908, 862258905, 2595165345, 7803321850, 23447714310, 70422834731, 211436276379, 634661150700, 1904721649632, 5715708452797

Offset: 1

Author

R. H. Hardin, Mar 11 2013

Keywords

• nonn

Comments

Column 2 of A222996.

A353047 is probably equal to 12 times this sequence. - N. J. A. Sloane, Jun 17 2022

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..33

Formula

Empirical: a(n) = 9*a(n-1) - 31*a(n-2) + 51*a(n-3) - 40*a(n-4) + 12*a(n-5).

Conjectures from Colin Barker, Feb 19 2018: (Start)

G.f.: x*(9 - 31*x + 51*x^2 - 40*x^3 + 12*x^4) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)).

a(n) = (-13 - 2^(6+n) + 3^(4+n) - 2*(1+2^(4+n))*n) / 4.

(End)