A280653 Triangle read by rows: T(n,k), n>=k>=1, is the number of acute triangles with integer coordinates that have a bounding box of size n X k.

0, 0, 0, 0, 0, 8, 0, 0, 6, 24, 0, 0, 6, 22, 40, 0, 0, 2, 20, 46, 64, 0, 0, 2, 20, 44, 70, 96, 0, 0, 2, 8, 42, 76, 98, 136, 0, 0, 2, 8, 34, 74, 104, 138, 176, 0, 0, 2, 8, 22, 72, 110, 148, 186, 208, 0, 0, 2, 4, 18, 56, 112, 146, 188, 234, 264, 0, 0, 2, 4, 18

Offset

1,6

Comments

It appears that the main diagonal is 8*A014811.

Links

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

Example

Triangle begins:
0
0,0
0,0,8
0,0,6,24
0,0,6,22,40
0,0,2,20,46,64
0,0,2,20,44,70,96
0,0,2,8,42,76,98,136
0,0,2,8,34,74,104,138,176
0,0,2,8,22,72,110,148,186,208
0,0,2,4,18,56,112,146,188,234,264
0,0,2,4,18,44,94,152,198,244,286,328
0,0,2,4,18,32,86,150,196,254,296,342,392
-----
For n=3, k=3:
o.o   o..   o..   .o.   .o.   .o.   ..o   ..o
...   ..o   ..o   o..   ..o   ...   o..   o..
.o.   o..   .o.   ..o   o..   o.o   .o.   ..o
so T(3,3)=8
-----
For n=4, k=3:
o..o   o..o   o...   .o..   ..o.   ...o
....   ....   ...o   ....   ....   o...
.o..   ..o.   o...   o..o   o..o   ...o
so T(4,3)=6
-----
For n=6, k=3:
o.....   .....o
.....o   o.....
o.....   .....o
so T(6,3)=2

Crossrefs

Cf. A190019.

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 A280652 for all obtuse triangles.

See A279432 for all triangles.

Sequence in context: A010771 A246560 A199064 * A274413 A369885 A167261

Adjacent sequences: A280650 A280651 A280652 * A280654 A280655 A280656

Keyword

nonn,tabl

Author

Lars Blomberg, Feb 25 2017

Status

approved