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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.

%I A280652 #10 Feb 28 2017 09:26:23
%S A280652 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,
%T A280652 88,104,0,36,76,104,112,120,132,140,0,42,86,130,136,152,160,184,180,0,
%U A280652 48,100,144,180,184,192,216,232,240,0,54,110,166,210,228,232
%N 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.
%H A280652 Lars Blomberg, <a href="/A280652/b280652.txt">Table of n, a(n) for n = 1..9870</a> (the first 140 rows)
%e A280652 Triangle begins:
%e A280652 0
%e A280652 0,0
%e A280652 0,4,8
%e A280652 0,12,16,20
%e A280652 0,18,32,36,36
%e A280652 0,24,48,56,60,72
%e A280652 0,30,62,76,84,88,104
%e A280652 0,36,76,104,112,120,132,140
%e A280652 0,42,86,130,136,152,160,184,180
%e A280652 0,48,100,144,180,184,192,216,232,240
%e A280652 0,54,110,166,210,228,232,252,268,284,312
%e A280652 0,60,124,188,240,272,272,296,316,336,352,372
%e A280652 0,66,134,202,258,314,328,332,352,372,400,428,436
%e A280652 0,72,148,224,288,352,380,400,408,432,448,480,508,536
%e A280652 -----
%e A280652 The obtuse angle is 'o'.
%e A280652 For n=3, k=2:
%e A280652 xo.   x..   .ox   ..x
%e A280652 ..x   .ox   x..   xo.
%e A280652 So T(3,2)=4
%e A280652 -----
%e A280652 For n=3, k=3:
%e A280652 xo.   x..   x..   x..   .ox   ..x   ..x   ..x
%e A280652 ...   o..   ..o   ...   ...   o..   ..o   ...
%e A280652 ..x   ..x   ..x   .ox   x..   x..   x..   xo.
%e A280652 So T(3,3)=8
%Y A280652 Cf. A190020.
%Y A280652 See A279415 for right isosceles triangles.
%Y A280652 See A280639 for obtuse isosceles triangles.
%Y A280652 See A279418 for acute isosceles triangles.
%Y A280652 See A279413 for all isosceles triangles.
%Y A280652 See A279433 for all right triangles.
%Y A280652 See A280653 for all acute triangles.
%Y A280652 See A279432 for all triangles.
%K A280652 nonn,tabl
%O A280652 1,5
%A A280652 _Lars Blomberg_, Feb 26 2017