A279415 Triangle read by rows: T(n,k), n>=k>=1, is the number of right isosceles triangles with integral coordinates that have a bounding box of size n X k.

0, 0, 4, 0, 2, 4, 0, 0, 4, 4, 0, 0, 2, 4, 4, 0, 0, 0, 4, 4, 4, 0, 0, 0, 2, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 2, 4, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 2, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 2, 4, 4

Offset

1,3

Links

Lars Blomberg, Table of n, a(n) for n = 1..9870 (the first 140 rows)

Example

Triangle begins:
0
0,4
0,2,4
0,0,4,4
0,0,2,4,4
0,0,0,4,4,4
0,0,0,2,4,4,4
0,0,0,0,4,4,4,4
0,0,0,0,2,4,4,4,4
0,0,0,0,0,4,4,4,4,4
0,0,0,0,0,2,4,4,4,4,4
0,0,0,0,0,0,4,4,4,4,4,4
0,0,0,0,0,0,2,4,4,4,4,4,4
-------
The right angle is 'o'.
For n=4, k=3:
x...   .o..   ..o.   ...x
...x   ...x   x...   x...
.o..   x...   ...x   ..o.
So T(4,3)=4
-------
For n=4, k=4:
o..x   x..o   x...   ...x
....   ....   ....   ....
....   ....   ....   ....
x...   ...x   o..x   x..o
So T(4,4)=4

Crossrefs

Cf. A187452.

See A280639 for obtuse isosceles triangles.

See A279418 for acute isosceles triangles.

See A279413 for all isosceles triangles.

See A279433 for all right triangles.

See A280652 for all obtuse triangles.

See A280653 for all acute triangles.

See A279432 for all triangles.

Sequence in context: A058997 A261164 A323982 * A201399 A145894 A366889

Adjacent sequences: A279412 A279413 A279414 * A279416 A279417 A279418

Keyword

nonn,tabl

Author

Lars Blomberg, Feb 27 2017

Status

approved