1,2

In Eisenstein's notation this is the array for m=1 and n=2; see example in given reference p. 42. The array for m=n=1 is A049456.

For n >= 1, the number of entries of row n is 2^(n-1)+1 with the difference sequence [2,1,2,4,8,16,...]. Row sums give 3*A007051(n-1).

The binary tree built from the rationals a(n,m)/a(n,m+1), m=0..2^(n-1), for each row n >= 1 gives the sub-tree of the (Eisenstein-)Stern-Brocot tree in the version of, e.g. Calkin and Wilf (for the reference see A002487 and the link) with root 1/2. The composition rule for this tree is i/j -> i/(i+j), (i+j)/j.

F. G. M. Eisenstein, Eine neue Gattung zahlentheoretischer Funktionen, welche von zwei Elementen abhaengen und durch gewisse lineare Funktional-Gleichungen definirt werden, Verhandlungen der Koenigl. Preuss. Akademie der Wiss. Berlin (1850) 36-42, Feb 18, 1850. Werke, II, pp. 705-711.

N. Calkin and H. S. Wilf, Recounting the Rationals, Amer. Math. Monthly, 107 (No. 4, 2000), pp. 360-363.

Index entries for sequences related to Stern's sequences

a(n, m)= a(n-1, m/2) if m is even, else a(n, m)= a(n-1, (m-1)/2)+a(n-1, (m+1)/2, a(1, 0)=1, a(1, 1)=2.

{1,2}; {1,3,2}; {1,4,3,5,2}; {1,5,4,7,3,8,5,7,2}; ...

This binary subtree of rationals is built from 1/2; 1/3,3/2; 1/4,4/3,3/5,5/2; ...

Sequence in context: A112383 A133404 A134627 this_sequence A131967 A137679 A152072

Adjacent sequences: A064878 A064879 A064880 this_sequence A064882 A064883 A064884

nonn,easy,tabf

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 19 2001