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

%I A057431 #23 Sep 06 2022 05:59:00
%S A057431 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,
%T A057431 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,
%U A057431 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
%N A057431 Obtained by reading first the numerator then the denominator of fractions in full Stern-Brocot tree (A007305/A047679).
%C A057431 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
%H A057431 Alois P. Heinz, <a href="/A057431/b057431.txt">Table of n, a(n) for n = 0..10000</a>
%H A057431 N. J. A. Sloane, <a href="/stern_brocot.html">Stern-Brocot or Farey Tree</a>
%H A057431 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%p A057431 F:= proc(n) option remember; local t;
%p A057431 t:= L -> [[L[1], [L[1][1]+L[2][1], L[1][2]+L[2][2]], L[2]],
%p A057431            [L[2], [L[2][1]+L[3][1], L[2][2]+L[3][2]], L[3]]][];
%p A057431       if n=0 then [[[ ], [0, 1], [ ]], [[ ], [1, 0], [ ]]]
%p A057431     elif n=1 then [[[0, 1], [1, 1], [1, 0]]]
%p A057431              else map(t, F(n-1))
%p A057431       fi
%p A057431     end:
%p A057431 aa:= n-> map(x-> x[], [seq(map(x-> x[2], F(j))[], j=0..n)])[]:
%p A057431 aa(7);   # aa(n) gives the first 2^(n+1)+2 terms
%p A057431 # _Alois P. Heinz_, Jan 13 2011
%t A057431 sbt[n_] := Module[{R, L, Y, w, u},
%t A057431    R = {{1, 0}, {1, 1}};
%t A057431    L = {{1, 1}, {0, 1}};
%t A057431    Y = {{1, 0}, {0, 1}};
%t A057431    w[b_] := Fold[#1.If[#2 == 0, L, R]&, Y, b];
%t A057431    u[a_] := {a[[2, 1]] + a[[2, 2]], a[[1, 1]] + a[[1, 2]]};
%t A057431    Map[u, Map[w, Tuples[{0, 1}, n]]]];
%t A057431 Join[{0, 1, 1, 0}, Table[sbt[n], {n, 0, 5}]] // Flatten (* _Jean-François Alcover_, Sep 06 2022, after _Peter Luschny_ in A007305 *)
%Y A057431 Cf. A007305, A047679, A007306, A002487, A057432.
%K A057431 nonn,look,easy
%O A057431 0,8
%A A057431 _N. J. A. Sloane_, Sep 08 2000
%E A057431 More terms from _Joshua Zucker_, May 11 2006