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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.
9
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
KEYWORD
nonn,tabl
AUTHOR
Lars Blomberg, Feb 25 2017
STATUS
approved