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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. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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 A227690 A063686

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

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Last modified July 23 08:59 EDT 2017. Contains 289686 sequences.