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

1,3

Comments

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

It appears that the main diagonal is 4*A000326.

Links

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

Example

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.

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.

Sequence in context: A158976 A211243 A181626 * A019127 A019207 A298449

Adjacent sequences: A279429 A279430 A279431 * A279433 A279434 A279435

Keyword

nonn,tabl

Author

Lars Blomberg, Feb 27 2017

Status

approved