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

0,13

Links

Table of n, a(n) for n=0..86.

Example

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...
...

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 *)

Crossrefs

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

Sequence in context: A224697 A052307 A067059 * A047996 A377060 A227690

Adjacent sequences: A049701 A049702 A049703 * A049705 A049706 A049707

Keyword

nonn,tabl

Author

Clark Kimberling

Extensions

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

Status

approved