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

1,4

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

Formula

Take each row of A049449 and append its reverse.

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

Crossrefs

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

Sequence in context: A328744 A345706 A132886 * A308483 A070871 A096115

Adjacent sequences: A119269 A119270 A119271 * A119273 A119274 A119275

Keyword

nonn,tabf

Author

Joshua Zucker, May 11 2006

Status

approved