A119272 Product of numerator and denominator in Stern-Brocot tree.

0, 0, 1, 2, 2, 3, 6, 6, 3, 4, 10, 15, 12, 12, 15, 10, 4, 5, 14, 24, 21, 28, 40, 35, 20, 20, 35, 40, 28, 21, 24, 14, 5, 6, 18, 33, 30, 44, 65, 60, 36, 45, 84, 104, 77, 70, 88, 63, 30, 30, 63, 88, 70, 77, 104, 84, 45, 36, 60, 65, 44, 30, 33, 18, 6, 7, 22, 42, 39, 60, 90, 85, 52, 70

Offset: 1

Author

Joshua Zucker, May 11 2006

Keywords

• nonn
• tabf

Comments

The sum of the reciprocals of each row (n > 0) is 1 (i.e., 1/1, 1/2 + 1/2, 1/3 + 1/6 + 1/6 + 1/3, 1/4 + ... + 1/4, 1/5 + ... + 1/5, ...). The cut-the-knot link gives credit to Pierre Lamothe for this observation.

Links

• Ivan Neretin, Table of n, a(n) for n = 1..4097
• Alexander Bogomolny, Cut-the-knot on Stern-Brocot trees

Crossrefs

Cf. A049449 (has the first half of each row), A007305 (numerators), A047679 (denominators).

Formula

Take each row of A049449 and append its reverse.

Also, a(n) = A007305(n-1)*A047679(n-3) for n>=3.