A279432 Triangle read by rows: T(n,k), n>=k>=1, is the number of triangles with integer coordinates that have a bounding box of size n X k.

0, 0, 4, 0, 10, 20, 0, 16, 34, 48, 0, 22, 44, 70, 88, 0, 28, 58, 88, 118, 140, 0, 34, 68, 102, 140, 178, 204, 0, 40, 82, 124, 166, 208, 250, 280, 0, 46, 92, 142, 184, 238, 284, 334, 368, 0, 52, 106, 156, 214, 268, 318, 376, 430, 468, 0, 58, 116, 178, 236, 290

Offset: 1

Author

Lars Blomberg, Feb 27 2017

Keywords

• nonn
• tabl

Comments

T(n,k) = A279433(n,k) + A280652(n,k) + A280653(n,k).

It appears that the main diagonal is 4*A000326.

Examples

			Triangle begins:
0
0,4
0,10,20
0,16,34,48
0,22,44,70,88
0,28,58,88,118,140
0,34,68,102,140,178,204
0,40,82,124,166,208,250,280
0,46,92,142,184,238,284,334,368
0,52,106,156,214,268,318,376,430,468
0,58,116,178,236,290,356,418,476,538,580
0,64,130,196,262,328,394,460,526,592,658,704
-----
A right angle is marked 'r', an obtuse one 'o'.
For n=2, k=2
rx   xr   x.   .x
x.   .x   rx   xr
So T(2,2)=4.
-----
For n=3, k=2
xo.   r.x   x.x   x.r   x..   x..   .ox   .r.   ..x   ..x
..x   x..   .r.   ..x   r.x   .ox   x..   x.x   xo.   x.r
So T(3,2)=10.
		

Links

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

Crossrefs

Cf. A045996.

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 A280653 for all acute triangles.