A137752 First numerator and then denominator (left to right) of Leibniz's harmonic-like triangle.

1, 1, 1, 2, 1, 2, 1, 3, 5, 6, 1, 3, 1, 4, 7, 12, 7, 12, 1, 4, 1, 5, 9, 20, 31, 30, 9, 20, 1, 5, 1, 6, 11, 30, 49, 60, 49, 60, 11, 30, 1, 6, 1, 7, 13, 42, 71, 105, 209, 140, 71, 105, 13, 42, 1, 7, 1, 8, 15, 56, 97, 168, 351, 280, 351, 280, 97, 168

Offset: 1

Author

Mohammad K. Azarian, Feb 10 2008

Keywords

• frac
• nonn
• tabf
• less

Comments

In this triangle the right-hand edge consists of the reciprocals of the positive integers. A number that is not in this edge is obtained by adding the number diagonally above it to the number to its immediate right. Note that in Leibniz's harmonic triangle we subtract the two numbers to get a number which is not on the right-hand edge.

Examples

			1/1;
1/2, 1/2;
1/3, 5/6, 1/3;
1/4, 7/12, 7/12, 1/4;
1/5, 9/20, 31/30, 9/20, 1/5;
		

Crossrefs

Cf. A003506; A007622; A046201; A046204; A046205; A046206; A046208; A046212.

Cf. A137753