A320543 (1/2) * number of ways to select 3 distinct points forming a triangle of unsigned area = 1 from a rectangle of grid points with side lengths j and k, written as triangle T(j,k), j<=k.

0, 3, 16, 8, 35, 72, 15, 62, 125, 212, 24, 95, 190, 319, 476, 35, 136, 269, 450, 669, 936, 48, 183, 360, 601, 892, 1245, 1652, 63, 238, 467, 776, 1149, 1602, 2123, 2724, 80, 299, 584, 967, 1430, 1991, 2636, 3379, 4188, 99, 368, 717, 1186, 1751, 2436, 3223, 4130, 5117, 6248

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Example

The triangle begins:
   0
   3  16
   8  35  72
  15  62 125 212
  24  95 190 319 476
  35 136 269 450 669 936
.
a(2) = T(1,2) = 3 = 6/2 because the following 6 triangles of area 1 can be made by selecting 3 grid points from the [0,1]X[0,2] rectangle:
  (0,0) (0,2) (1,0),
  (0,0) (0,2) (1,1),
  (0,0) (0,2) (1,2),
  (0,0) (1,0) (1,2),
  (0,1) (1,0) (1,2),
  (0,2) (1,0) (1,2).

Crossrefs

Cf. A005563, A320539, A320541, A320544.

Sequence in context: A286697 A286021 A286649 * A213847 A195883 A272329

Adjacent sequences: A320540 A320541 A320542 * A320544 A320545 A320546

Keyword

nonn,tabl

Author

Hugo Pfoertner, Oct 16 2018

Status

approved