A189808 Number of right triangles on a (n+1) X 4 grid.

28, 94, 200, 342, 524, 732, 972, 1236, 1524, 1840, 2180, 2544, 2932, 3344, 3780, 4240, 4724, 5232, 5764, 6320, 6900, 7504, 8132, 8784, 9460, 10160, 10884, 11632, 12404, 13200, 14020, 14864, 15732, 16624, 17540, 18480, 19444, 20432, 21444, 22480, 23540

Offset: 1

Author

R. H. Hardin, Apr 28 2011

Keywords

• nonn

Comments

Column 3 of A189814.

Examples

			Some solutions for n=3:
..3..1....2..2....0..0....2..1....2..0....3..3....1..1....1..1....3..2....1..1
..0..1....3..1....0..3....2..2....0..0....0..3....1..2....0..2....2..2....2..0
..3..2....3..3....2..0....4..1....2..3....3..0....4..1....3..3....3..3....3..3
		

Links

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

Crossrefs

Cf. A189814.

Formula

Empirical: a(n) = 12*n^2 + 88*n - 240 for n>8.

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

G.f.: 2*x*(14 + 5*x + x^2 - 2*x^3 + 2*x^4 - 7*x^5 + 3*x^6 - 4*x^7 + 2*x^9 - 2*x^10) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.

(End)