login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A064884 Eisenstein array Ei(3,1). 0
3, 1, 3, 4, 1, 3, 7, 4, 5, 1, 3, 10, 7, 11, 4, 9, 5, 6, 1, 3, 13, 10, 17, 7, 18, 11, 15, 4, 13, 9, 14, 5, 11, 6, 7, 1, 3, 16, 13, 23, 10, 27, 17, 24, 7, 25, 18, 29, 11, 26, 15, 19, 4, 17, 13, 22, 9, 23, 14, 19, 5, 16, 11, 17, 6, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

In Eisenstein's notation this is the array for m=3 and n=1; see pp. 41-42 of the Eisenstein reference given for A064881. This is identical with the array for m=1,n=3, given in A064883, read backwards. 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 4*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, also for the Wilf link) with root 3/1. The composition rule of this tree is i/j -> i/(i+j), (i+j)/j.

LINKS

Table of n, a(n) for n=1..66.

Index entries for sequences related to Stern's sequences

FORMULA

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)=3, a(1, 1)=1.

EXAMPLE

{3,1};

{3,4,1};

{3,7,4,5,1};

{3,10,7,11,4,9,5,6,1}; ...

This binary subtree of rationals is built from

3/1;

3/4,4/1;

3/7,7/4,4/5,5/1; ...

MATHEMATICA

nmax = 6; a[n_, m_?EvenQ] := a[n-1, m/2]; a[n_, m_?OddQ] := a[n, m] = a[n-1, (m-1)/2] + a[n-1, (m+1)/2]; a[1, 0] = 3; a[1, 1] = 1; Flatten[Table[a[n, m], {n, 1, nmax}, {m, 0, 2^(n-1)}]] (* Jean-Fran├žois Alcover, Sep 28 2011 *)

eisen = Most@Flatten@Transpose[{#, # + RotateLeft[#]}] &;

Flatten@NestList[eisen, {3, 1}, 6] (* Harlan J. Brothers, Feb 18 2015 *)

CROSSREFS

Sequence in context: A107638 A245093 A104765 * A093560 A173934 A131504

Adjacent sequences:  A064881 A064882 A064883 * A064885 A064886 A064887

KEYWORD

nonn,easy,tabf

AUTHOR

Wolfdieter Lang, Oct 19 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 24 18:24 EST 2018. Contains 299628 sequences. (Running on oeis4.)