A189809 Number of right triangles on an (n+1) X 5 grid.

46, 158, 342, 596, 926, 1308, 1754, 2250, 2794, 3390, 4026, 4702, 5426, 6190, 6994, 7838, 8726, 9654, 10622, 11630, 12678, 13766, 14894, 16062, 17270, 18518, 19806, 21134, 22502, 23910, 25358, 26846, 28374, 29942, 31550, 33198, 34886, 36614, 38382

Offset

1,1

Comments

Column 4 of A189814.

Links

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

Formula

Empirical: a(n) = 20*n^2 + 228*n - 930 for n>15.

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

G.f.: 2*x*(23 + 10*x + 3*x^2 - x^3 + 3*x^4 - 12*x^5 + 6*x^6 - 7*x^7 - x^8 + 2*x^9 - 6*x^10 + 4*x^12 - 4*x^13 + 2*x^16 - 2*x^17) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11.

(End)

Example

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

Crossrefs

Cf. A189814.

Sequence in context: A044378 A044759 A223607 * A350556 A251467 A251460

Adjacent sequences: A189806 A189807 A189808 * A189810 A189811 A189812

Keyword

nonn

Author

R. H. Hardin, Apr 28 2011

Status

approved