A279418 Triangle read by rows: T(n,k), n>=k>=1, is the number of acute isosceles triangles with integer coordinates that have a bounding box of size n X k.

0, 0, 0, 0, 0, 8, 0, 0, 2, 8, 0, 0, 2, 2, 16, 0, 0, 2, 4, 6, 16, 0, 0, 2, 0, 4, 2, 24, 0, 0, 2, 0, 2, 4, 6, 24, 0, 0, 2, 0, 6, 6, 4, 6, 40, 0, 0, 2, 0, 2, 0, 6, 4, 6, 40, 0, 0, 2, 0, 2, 0, 8, 2, 8, 2, 40, 0, 0, 2, 0, 2, 4, 2, 8, 2, 4, 10, 40, 0, 0, 2, 0, 2, 0

Offset: 1

Author

Lars Blomberg, Feb 27 2017

Keywords

• nonn
• tabl

Examples

			Triangle begins:
0
0,0
0,0,8
0,0,2,8
0,0,2,2,16
0,0,2,4,6,16
0,0,2,0,4,2,24
0,0,2,0,2,4,6,24
0,0,2,0,6,6,4,6,40
0,0,2,0,2,0,6,4,6,40
0,0,2,0,2,0,8,2,8,2,40
0,0,2,0,2,4,2,8,2,4,10,40
0,0,2,0,2,0,2,2,8,10,8,10,48
0,0,2,0,2,4,2,4,10,0,2,8,14,48
0,0,2,0,2,0,6,0,4,6,12,6,8,6,56
0,0,2,0,2,0,2,0,2,8,2,0,6,8,10,56
------
The vertex between the two equal sides is 'o'.
For n=3, k=3:
x.x   x..   o..   .x.   .x.   .o.   ..o   ..x
...   ..o   ..x   x..   ..x   ...   x..   o..
.o.   x..   .x.   ..o   o..   x.x   .x.   ..x
So T(3,3)=8
------
For n=6, k=4:
x....o   o....x   .x....   ....x.
......   ......   ......   ......
......   ......   ......   ......
.x....   ....x.   x....o   o....x
So T(6,4)=4
		

Links

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

Crossrefs

Cf. A190317.

See A279415 for right isosceles triangles.

See A280639 for obtuse 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.