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Triangle read by rows: T(n,k), n>=k>=1, is the number of right triangles with integral coordinates that have a bounding box of size n X k.
9

%I #10 Feb 28 2017 09:26:13

%S 0,0,4,0,6,4,0,4,12,4,0,4,6,12,12,0,4,8,12,12,4,0,4,4,6,12,20,4,0,4,4,

%T 12,12,12,20,4,0,4,4,4,14,12,20,12,12,0,4,4,4,12,12,16,12,12,20,0,4,4,

%U 8,8,6,12,20,20,20,4,0,4,4,4,4,12,28,12,12,12

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

%H Lars Blomberg, <a href="/A279433/b279433.txt">Table of n, a(n) for n = 1..9870</a> (the first 140 rows)

%e Triangle begins:

%e 0

%e 0,4

%e 0,6,4

%e 0,4,12,4

%e 0,4,6,12,12

%e 0,4,8,12,12,4

%e 0,4,4,6,12,20,4

%e 0,4,4,12,12,12,20,4

%e 0,4,4,4,14,12,20,12,12

%e 0,4,4,4,12,12,16,12,12,20

%e 0,4,4,8,8,6,12,20,20,20,4

%e 0,4,4,4,4,12,28,12,12,12,20,4

%e 0,4,4,4,4,12,6,20,20,16,20,20,12

%e 0,4,4,4,12,4,24,12,12,12,20,12,20,4

%e 0,4,4,4,4,4,12,6,28,20,12,20,20,20,4

%e 0,4,4,4,4,4,8,12,20,20,12,20,12,20,28,4

%e 0,4,4,4,4,12,4,12,18,12,20,12,28,12,20,20,28

%e -----

%e The right angle is 'o'.

%e For n=2, k=2:

%e ox xo x. .x

%e x. .x ox xo

%e So T(2,2)=4

%e -----

%e For n=3, k=2:

%e o.x x.x x.o x.. .o. ..x

%e x.. .o. ..x o.x x.x x.o

%e So T(3,2)=6

%Y Cf. A077435.

%Y See A279415 for right isosceles triangles.

%Y See A280639 for obtuse isosceles triangles.

%Y See A279418 for acute isosceles triangles.

%Y See A279413 for all isosceles triangles.

%Y See A280652 for all obtuse triangles.

%Y See A280653 for all acute triangles.

%Y See A279432 for all triangles.

%K nonn,tabl

%O 1,3

%A _Lars Blomberg_, Feb 27 2017