A074234 Number of nodes of integer unit lattice covered by integer right triangles.

12, 36, 43, 72, 79, 106, 120, 146, 180, 213, 245, 250, 252, 278, 309, 336, 376, 380, 432, 532, 540, 559, 597, 607, 660, 694, 786, 792, 815, 822, 910, 918, 920, 936, 1001, 1036, 1069, 1092, 1158, 1260, 1321, 1412, 1419, 1432, 1440, 1478, 1561, 1595, 1632

Offset

1,1

Comments

Let the coordinates of the vertices of the integer right triangle with legs 3,4 be (0,0), (3,0) and (0,4). Then the number of points with integer coordinates, including those on the sides, is 12. This is the maximal number of nodes covered by the triangle 3,4,5. Increasing all three lengths m times leads to a number of covered nodes equal to 6m(m+1).

Links

Table of n, a(n) for n=1..49.

Example

a(1) = 12 because integer right triangle with legs 3,4 can cover a maximum of 12 nodes of the integer unit lattice. a(3) = 43 because integer right triangle with legs 5,12 can cover a maximum of 43 nodes of the integer unit lattice.

Crossrefs

Sequence in context: A203378 A073543 A349020 * A076515 A371415 A039317

Adjacent sequences: A074231 A074232 A074233 * A074235 A074236 A074237

Keyword

nonn

Author

Zak Seidov, Sep 18 2002

Status

approved