A057431 Obtained by reading first the numerator then the denominator of fractions in full Stern-Brocot tree (A007305/A047679).

0, 1, 1, 0, 1, 1, 1, 2, 2, 1, 1, 3, 2, 3, 3, 2, 3, 1, 1, 4, 2, 5, 3, 5, 3, 4, 4, 3, 5, 3, 5, 2, 4, 1, 1, 5, 2, 7, 3, 8, 3, 7, 4, 7, 5, 8, 5, 7, 4, 5, 5, 4, 7, 5, 8, 5, 7, 4, 7, 3, 8, 3, 7, 2, 5, 1, 1, 6, 2, 9, 3, 11, 3, 10, 4, 11, 5, 13, 5, 12, 4, 9, 5, 9, 7, 12, 8, 13, 7, 11, 7, 10, 8, 11, 7, 9, 5, 6, 6, 5

Offset: 0

Author

N. J. A. Sloane, Sep 08 2000

Keywords

• nonn
• look
• easy

Comments

When presented in this way, every row (e.g. row 3, 1 3 2 3 3 2 3 1) is a palindrome. - Joshua Zucker, May 11 2006

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• N. J. A. Sloane, Stern-Brocot or Farey Tree
• Index entries for sequences related to Stern's sequences

Crossrefs

Cf. A007305, A047679, A007306, A002487, A057432.

Programs

Maple

F:= proc(n) option remember; local t;
t:= L -> [[L[1], [L[1][1]+L[2][1], L[1][2]+L[2][2]], L[2]],
           [L[2], [L[2][1]+L[3][1], L[2][2]+L[3][2]], L[3]]][];
      if n=0 then [[[ ], [0, 1], [ ]], [[ ], [1, 0], [ ]]]
    elif n=1 then [[[0, 1], [1, 1], [1, 0]]]
             else map(t, F(n-1))
      fi
    end:
aa:= n-> map(x-> x[], [seq(map(x-> x[2], F(j))[], j=0..n)])[]:
aa(7);   # aa(n) gives the first 2^(n+1)+2 terms
# Alois P. Heinz, Jan 13 2011

Mathematica

sbt[n_] := Module[{R, L, Y, w, u},
   R = {{1, 0}, {1, 1}};
   L = {{1, 1}, {0, 1}};
   Y = {{1, 0}, {0, 1}};
   w[b_] := Fold[#1.If[#2 == 0, L, R]&, Y, b];
   u[a_] := {a[[2, 1]] + a[[2, 2]], a[[1, 1]] + a[[1, 2]]};
   Map[u, Map[w, Tuples[{0, 1}, n]]]];
Join[{0, 1, 1, 0}, Table[sbt[n], {n, 0, 5}]] // Flatten (* Jean-François Alcover, Sep 06 2022, after Peter Luschny in A007305 *)

Extensions

More terms from Joshua Zucker, May 11 2006