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 A049455 Triangle read by rows: T(n,k) = numerator of fraction in k-th term of n-th row of variant of Farey series. 11
 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; text; internal format)
 OFFSET 1,9 COMMENTS Stern's diatomic array read by rows (version 4, the 0,1 version). 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. Largest term of n-th row = A000045(n), Fibonacci numbers. - Reinhard Zumkeller, Apr 02 2014 REFERENCES 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. LINKS Reinhard Zumkeller, Rows n = 1..13 of table, flattened 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). Jennifer Lansing, Largest Values for the Stern Sequence, J. Integer Seqs., 17 (2014), #14.7.5. M. Shrader-Frechette, Modified Farey sequences and continued fractions, Math. Mag., 54 (1981), 60-63. N. J. A. Sloane, Stern-Brocot or Farey Tree 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 The 0,1 version of Stern's diatomic array (cf. A002487) begins: 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, 0,1,1,2,1,3,2,3,1,4,3,5,2,5,3,4,1,5,4,7,3,8,5,7,2,7,5,3,3,7,4,5,1, ... PROG (Haskell) import Data.List (transpose) import Data.Ratio ((%), numerator, denominator) a049455 n k = a049455_tabf !! (n-1) !! (k-1) a049455_row n = a049455_tabf !! (n-1) a049455_tabf = map (map numerator) \$ iterate    (\row -> concat \$ transpose [row, zipWith (+/+) row \$ tail row]) [0, 1]    where u +/+ v = (numerator u + numerator v) %                    (denominator u + denominator v) -- Reinhard Zumkeller, Apr 02 2014 (PARI) mediant(x, y) = (numerator(x)+numerator(y))/(denominator(x)+denominator(y)); newrow(rowa) = {my(rowb = []); for (i=1, #rowa-1, rowb = concat(rowb, rowa[i]); rowb = concat(rowb, mediant(rowa[i], rowa[i+1])); ); concat(rowb, rowa[#rowa]); } rows(nn) = {my(rowa); for (n=1, nn, if (n==1, rowa = [0, 1], rowa = newrow(rowa)); print(apply(x->numerator(x), rowa)); ); } \\ Michel Marcus, Apr 03 2019 CROSSREFS Cf. A049456. Also A007305, A007306, A006842, A006843, A070878, A070879. Row sums are A007051. Cf. A000051 (row lengths), A293165 (distinct terms). Sequence in context: A126304 A280522 A324796 * A322975 A133734 A109702 Adjacent sequences:  A049452 A049453 A049454 * A049456 A049457 A049458 KEYWORD nonn,easy,tabf,frac,look AUTHOR EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Apr 12 2000 STATUS approved

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Last modified October 20 10:32 EDT 2019. Contains 328257 sequences. (Running on oeis4.)