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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.
9
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
KEYWORD
nonn,tabl
AUTHOR
Lars Blomberg, Feb 26 2017
STATUS
approved