A354698 T(n,k) is the number of points with integer coordinates strictly inside the triangle with vertices (0,0), (n,0), (n,k), where T(n,k) is a triangle read by rows, 2 <= k <= n.

0, 1, 1, 1, 3, 3, 2, 4, 6, 6, 2, 4, 7, 10, 10, 3, 6, 9, 12, 15, 15, 3, 7, 9, 14, 17, 21, 21, 4, 7, 12, 16, 19, 24, 28, 28, 4, 9, 13, 16, 22, 27, 31, 36, 36, 5, 10, 15, 20, 25, 30, 35, 40, 45, 45, 5, 10, 15, 22, 25, 33, 37, 43, 49, 55, 55, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 66

Offset: 2

Author

Hugo Pfoertner, Jun 06 2022

Keywords

• nonn
• tabl
• easy

Comments

T(n,n) = T(n,n-1) because all grid points with m = n lie on a side of the triangle and thus not strictly inside.

Examples

			The triangle begins:
  0;
  1,  1;
  1,  3,  3;
  2,  4,  6,  6;
  2,  4,  7, 10, 10;
  3,  6,  9, 12, 15, 15;
  3,  7,  9, 14, 17, 21, 21;
  4,  7, 12, 16, 19, 24, 28, 28;
  4,  9, 13, 16, 22, 27, 31, 36, 36;
  5, 10, 15, 20, 25, 30, 35, 40, 45, 45;
  5, 10, 15, 22, 25, 33, 37, 43, 49, 55, 55
		

Crossrefs

Cf. A000217 (right diagonal), A074148 (3rd diagonal).

Cf. A004526 (column 2), A117571 (column 3).

Programs

PARI

T(n, m) = sum(i=1, n-1, sum(j=1, m-1, (i/j > n/m))); \\ Michel Marcus, Jun 07 2022