A280652 Triangle read by rows: T(n,k), n>=k>=1, is the number of obtuse triangles with integer coordinates that have a bounding box of size n X k.

0, 0, 0, 0, 4, 8, 0, 12, 16, 20, 0, 18, 32, 36, 36, 0, 24, 48, 56, 60, 72, 0, 30, 62, 76, 84, 88, 104, 0, 36, 76, 104, 112, 120, 132, 140, 0, 42, 86, 130, 136, 152, 160, 184, 180, 0, 48, 100, 144, 180, 184, 192, 216, 232, 240, 0, 54, 110, 166, 210, 228, 232

Offset: 1

Author

Lars Blomberg, Feb 26 2017

Keywords

• nonn
• tabl

Examples

			Triangle begins:
0
0,0
0,4,8
0,12,16,20
0,18,32,36,36
0,24,48,56,60,72
0,30,62,76,84,88,104
0,36,76,104,112,120,132,140
0,42,86,130,136,152,160,184,180
0,48,100,144,180,184,192,216,232,240
0,54,110,166,210,228,232,252,268,284,312
0,60,124,188,240,272,272,296,316,336,352,372
0,66,134,202,258,314,328,332,352,372,400,428,436
0,72,148,224,288,352,380,400,408,432,448,480,508,536
-----
The obtuse angle is 'o'.
For n=3, k=2:
xo.   x..   .ox   ..x
..x   .ox   x..   xo.
So T(3,2)=4
-----
For n=3, k=3:
xo.   x..   x..   x..   .ox   ..x   ..x   ..x
...   o..   ..o   ...   ...   o..   ..o   ...
..x   ..x   ..x   .ox   x..   x..   x..   xo.
So T(3,3)=8
		

Links

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

Crossrefs

Cf. A190020.

See A279415 for right isosceles triangles.

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 A280653 for all acute triangles.

See A279432 for all triangles.