cp's OEIS Frontend

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.

%I A279432 #9 Feb 28 2017 09:26:06
%S A279432 0,0,4,0,10,20,0,16,34,48,0,22,44,70,88,0,28,58,88,118,140,0,34,68,
%T A279432 102,140,178,204,0,40,82,124,166,208,250,280,0,46,92,142,184,238,284,
%U A279432 334,368,0,52,106,156,214,268,318,376,430,468,0,58,116,178,236,290
%N 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.
%C A279432 T(n,k) = A279433(n,k) + A280652(n,k) + A280653(n,k).
%C A279432 It appears that the main diagonal is 4*A000326.
%H A279432 Lars Blomberg, <a href="/A279432/b279432.txt">Table of n, a(n) for n = 1..9870</a> (the first 140 rows)
%e A279432 Triangle begins:
%e A279432 0
%e A279432 0,4
%e A279432 0,10,20
%e A279432 0,16,34,48
%e A279432 0,22,44,70,88
%e A279432 0,28,58,88,118,140
%e A279432 0,34,68,102,140,178,204
%e A279432 0,40,82,124,166,208,250,280
%e A279432 0,46,92,142,184,238,284,334,368
%e A279432 0,52,106,156,214,268,318,376,430,468
%e A279432 0,58,116,178,236,290,356,418,476,538,580
%e A279432 0,64,130,196,262,328,394,460,526,592,658,704
%e A279432 -----
%e A279432 A right angle is marked 'r', an obtuse one 'o'.
%e A279432 For n=2, k=2
%e A279432 rx   xr   x.   .x
%e A279432 x.   .x   rx   xr
%e A279432 So T(2,2)=4.
%e A279432 -----
%e A279432 For n=3, k=2
%e A279432 xo.   r.x   x.x   x.r   x..   x..   .ox   .r.   ..x   ..x
%e A279432 ..x   x..   .r.   ..x   r.x   .ox   x..   x.x   xo.   x.r
%e A279432 So T(3,2)=10.
%Y A279432 Cf. A045996.
%Y A279432 See A279415 for right isosceles triangles.
%Y A279432 See A280639 for obtuse isosceles triangles.
%Y A279432 See A279418 for acute isosceles triangles.
%Y A279432 See A279413 for all isosceles triangles.
%Y A279432 See A279433 for all right triangles.
%Y A279432 See A280652 for all obtuse triangles.
%Y A279432 See A280653 for all acute triangles.
%K A279432 nonn,tabl
%O A279432 1,3
%A A279432 _Lars Blomberg_, Feb 27 2017