|
| |
|
|
A049455
|
|
Triangle read by rows: T(n,k) = numerator of fraction in k-th term of n-th row of variant of Farey series.
|
|
9
| |
|
|
0, 1, 0, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 2, 1, 3, 2, 3, 1, 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,9
|
|
|
COMMENTS
| Stern's diatomic array read by rows (version 4).
This sequence divided by A049456 gives another version of the Stern-Brocot tree.
Row n has length 2^n + 1.
Define mediant of a/b and c/d to be (a+c)/(b+d). We get A006842/A006843 if we omit terms from n-th row in which denominator exceeds n.
|
|
|
REFERENCES
| C. Giuli and R. Giuli, A primer on Stern's diatomic sequence, Fib. Quart., 17 (1979), 103-108, 246-248 and 318-320 (but beware errors).
J. C. Lagarias, Number Theory and Dynamical Systems, pp. 35-72 of S. A. Burr, ed., The Unreasonable Effectiveness of Number Theory, Proc. Sympos. Appl. Math., 46 (1992). Amer. Math. Soc.
W. J. LeVeque, Topics in Number Theory. Addison-Wesley, Reading, MA, 2 vols., 1956, Vol. 1, p. 154.
M. Shrader-Frechette, Modified Farey sequences and continued fractions, Math. Mag., 54 (1981), 60-63.
|
|
|
LINKS
| N. J. A. Sloane, Stern-Brocot or Farey Tree
Index entries for sequences related to Stern's sequences
|
|
|
FORMULA
| Row 1 is 0/1, 1/1. Obtain row n from row n-1 by inserting mediants between each pair of terms.
|
|
|
EXAMPLE
| 0/1, 1/1; 0/1, 1/2, 1/1; 0/1, 1/3, 1/2, 2/3, 1/1; 0/1, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 1/1; 0/1, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, ... = A049455/A049456
|
|
|
CROSSREFS
| Cf. A049456. Also A007305, A007306, A006842, A006843, A070878, A070879.
Row sums are A007051.
Sequence in context: A054070 A204172 A126304 * A133734 A109702 A115412
Adjacent sequences: A049452 A049453 A049454 * A049456 A049457 A049458
|
|
|
KEYWORD
| nonn,easy,tabf,frac
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Apr 12 2000
|
| |
|
|
