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.

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, 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, 5, 7, 9, 10, 10, 9, 7, 5, 1, 1, 1, 1, 6, 9, 11, 11, 12, 11, 11

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• tabl

Examples

			The array begins:
0 1 1 1 1 1 1 1 1...
1 1 1 1 1 1 1 1 1...
1 1 2 2 3 3 4 4 5...
1 1 2 4 4 5 6 6 7...
1 1 3 4 6 6 8 9 11...
...
		

Crossrefs

Cf. A049600, A049615, A049639, A049687, A049695, A049702. Cf. A049706-A049709. Main diagonal: A002088.

Programs

Mathematica

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/@#&]]]];
(*Table[t[i,j], {i,0,10}, {j,0,10}]//TableForm*)
Flatten@Table[t[j,i-j], {i,0,20}, {j,0,i}]
(* Andrey Zabolotskiy, Jun 09 2017 *)

Extensions

Name corrected by Michel Marcus and Andrey Zabolotskiy, Jun 10 2017