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

1,6

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
0,0,2,8
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

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.

Sequence in context: A171918 A265117 A345159 * A157244 A154191 A010771

Adjacent sequences: A279415 A279416 A279417 * A279419 A279420 A279421

Keyword

nonn,tabl

Author

Lars Blomberg, Feb 27 2017

Status

approved