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

1,4

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.

Links

Table of n, a(n) for n=1..68.

Example

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

Sequence in context: A226212 A233439 A256600 * A331917 A328318 A081169

Adjacent sequences: A137749 A137750 A137751 * A137753 A137754 A137755

Keyword

frac,nonn,tabf,less

Author

Mohammad K. Azarian, Feb 10 2008

Status

approved