A189807 Number of right triangles on an (n+1) X 3 grid.

14, 44, 94, 158, 238, 330, 434, 550, 678, 818, 970, 1134, 1310, 1498, 1698, 1910, 2134, 2370, 2618, 2878, 3150, 3434, 3730, 4038, 4358, 4690, 5034, 5390, 5758, 6138, 6530, 6934, 7350, 7778, 8218, 8670, 9134, 9610, 10098, 10598, 11110, 11634, 12170, 12718

Offset

1,1

Comments

Column 2 of A189814.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 6*n^2 + 26*n - 42 for n>3.

Conjectures from Colin Barker, May 03 2018: (Start)

G.f.: 2*x*(7 + x + 2*x^2 - 3*x^3 + x^4 - 2*x^5) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.

(End)

Example

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

Crossrefs

Cf. A189814.

Sequence in context: A089031 A265152 A033587 * A009942 A031130 A215199

Adjacent sequences: A189804 A189805 A189806 * A189808 A189809 A189810

Keyword

nonn

Author

R. H. Hardin, Apr 28 2011

Status

approved