1,3

The redundant Stern-Brocot structure is constructed row by row: insert between consecutive terms of the full Stern-Brocot tree their mediant (non-reduced), where the mediant of s/t and u/v = (s+u)/(t+v);

a(2^n-n+2*k) = A007305(2^(n-1)+k+2) for 0<=k<2^(n-1);

a(2^n-n+2*k-1) = A007305(2^(n-1)+k-1+2) + A007305(2^(n-1)+k+2) for 0<k<2^(n-1);

the graph of this structure describes an interesting ternary representation of the positive rational numbers;

A060188(k+2) = Sum(a(i): 2^k <= i < 2^(k+1)).

Milad Niqui, Formalising Exact Arithmetic, Ph.D. thesis, Radboud Universiteit Nijmegen, IPA Dissertation Series 2004-10, 2.6, p.65f .

Milad Niqui, Formalising Exact Arithmetic

Index entries for sequences related to Stern's sequences

[0/1] . . . . . . . . . . . . . . . . . . . . . . . . . . . [1/0]

.............................. 1/1

............. 1/2 ............ 3/3 ............ 2/1

..... 1/3 ... 3/6 .... 2/3 ... 5/5 ... 3/2 .... 6/3 ... 3/1

. 1/4 3/9 2/5 5/10 3/5 6/9 3/4 7/7 4/3 9/6 5/3 10/5 5/2 9/3 4/1.

Sequence in context: A087818 A112746 A107460 this_sequence A128262 A140414 A129514

Adjacent sequences: A152972 A152973 A152974 this_sequence A152976 A152977 A152978

frac,nonn,tabf

Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 22 2008