This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A049704 #13 Jun 10 2017 08:06:53
%S A049704 0,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,2,1,1,1,1,3,4,3,1,1,1,1,3,4,4,3,
%T A049704 1,1,1,1,4,5,6,5,4,1,1,1,1,4,6,6,6,6,4,1,1,1,1,5,6,8,10,8,6,5,1,1,1,1,
%U A049704 5,7,9,10,10,9,7,5,1,1,1,1,6,9,11,11,12,11,11
%N A049704 Array T read by antidiagonals; T(i,j)=number of nonnegative slopes of lines determined by two points in the triangular set {(x,y): 0<=x<=i, 0<=y<=j-j*x/i} of lattice points.
%e A049704 The array begins:
%e A049704 0 1 1 1 1 1 1 1 1...
%e A049704 1 1 1 1 1 1 1 1 1...
%e A049704 1 1 2 2 3 3 4 4 5...
%e A049704 1 1 2 4 4 5 6 6 7...
%e A049704 1 1 3 4 6 6 8 9 11...
%e A049704 ...
%t A049704 t[i_,j_] := If[i==0||j==0, 1-KroneckerDelta[i+j], 1+Length[Union[Divide@@#& /@ Select[-Subtract@@@Subsets[Flatten[Table[{x,y}, {x,0,i}, {y,0,j-j*x/i}], 1], {2}], And@@Positive/@#&]]]];
%t A049704 (*Table[t[i,j], {i,0,10}, {j,0,10}]//TableForm*)
%t A049704 Flatten@Table[t[j,i-j], {i,0,20}, {j,0,i}]
%t A049704 (* _Andrey Zabolotskiy_, Jun 09 2017 *)
%Y A049704 Cf. A049600, A049615, A049639, A049687, A049695, A049702. Cf. A049706-A049709. Main diagonal: A002088.
%K A049704 nonn,tabl
%O A049704 0,13
%A A049704 _Clark Kimberling_
%E A049704 Name corrected by _Michel Marcus_ and _Andrey Zabolotskiy_, Jun 10 2017