A245251 Triangle T(a,b) read by rows: sum_{k=1..a-1} floor(k*b/a).

0, 0, 1, 0, 1, 3, 0, 2, 3, 6, 0, 2, 4, 6, 10, 0, 3, 6, 8, 10, 15, 0, 3, 6, 9, 12, 15, 21, 0, 4, 7, 12, 14, 18, 21, 28, 0, 4, 9, 12, 16, 21, 24, 28, 36, 0, 5, 9, 14, 20, 23, 27, 32, 36, 45, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 55, 0, 6, 12, 18, 22, 30, 33, 40, 45, 50, 55, 66, 0, 6, 12, 18, 24, 30, 36, 45

Offset: 1

Author

Jaimal Ichharam, Jul 15 2014

Keywords

• nonn
• tabl
• easy

Examples

			  0;
  0   1;
  0   1   3;
  0   2   3   6;
  0   2   4   6  10;
  0   3   6   8  10  15;
  0   3   6   9  12  15  21;
  0   4   7  12  14  18  21  28;
  0   4   9  12  16  21  24  28  36;
  0   5   9  14  20  23  27  32  36  45;
		

Crossrefs

Cf. A000217 (right diagonal).

Programs

Mathematica

Table[Sum[Floor[(k b)/a], {k, a-1}], {a, 20}, {b, a}] // Flatten

Formula

T(a, b) = (a*b-a-b+gcd(a,b))/2.

T(n, n) = n*(n-1)/2.