A049449 -id:A049449 - cp's OEIS frontend

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

Joshua Zucker, May 11 2006

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.

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

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

Take each row of A049449 and append its reverse.

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

A335699 Irregular tree read by rows: take the Stern-Brocot tree A007305(n)/A007306(n) and set a(n) = A007306(n) - A007305(n) mod 3.

Original entry on oeis.org

1, 0, 1, 2, 1, 0, 0, 2, 1, 1, 2, 2, 1, 0, 0, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 0, 0, 2, 1, 0, 0, 2, 1, 2, 1, 0, 0, 0, 0, 1, 2, 1, 2, 0, 0, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 0, 0, 2, 1, 1, 2, 2, 1, 0, 0, 2, 1, 2, 1, 0, 0, 2

Offset: 0

N. J. A. Sloane, Aug 05 2020

			The initial rows of the tree are 1,0 // 1 // 2,1 // 0,0,2,1 // 1,2,2,1,0,0,2,1 // ...

Kiana Mittelstaedt, A Stochastic Approach to Eulerian Numbers, arXiv:1902.03195 [math.CO], 2019. Also Amer. Math. Mnthly, 127:7 (2020), 618-628. See Fig. 5. Note that this author has omitted the two initial terms.

Cf. A002487, A007305, A007306, A049448, A049449, A057431.

cp's OEIS Frontend

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

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