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

1,5

Links

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

Example

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

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.

Sequence in context: A125507 A198583 A244123 * A104538 A120580 A205508

Adjacent sequences: A280649 A280650 A280651 * A280653 A280654 A280655

Keyword

nonn,tabl

Author

Lars Blomberg, Feb 26 2017

Status

approved