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A064882 Eisenstein array Ei(2,1). 0
2, 1, 2, 3, 1, 2, 5, 3, 4, 1, 2, 7, 5, 8, 3, 7, 4, 5, 1, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4, 9, 5, 6, 1, 2, 11, 9, 16, 7, 19, 12, 17, 5, 18, 13, 21, 8, 19, 11, 14, 3, 13, 10, 17, 7, 18, 11, 15, 4, 13, 9, 14, 5, 11, 6, 7, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

In Eisenstein's notation this is the array for m=2 and n=1; see pp. 41-2 of the Eisenstein reference given for A064881. This is identical with the array for m=1,n=2, given in A064881, 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 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 (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 2/1. The composition rule of this tree is i/j -> i/(i+j), (i+j)/j.

LINKS

Table of n, a(n) for n=1..69.

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)=2, a(1, 1)=1.

EXAMPLE

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

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

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] = 2; a[1, 1] = 1; Flatten[ Table[ a[n, m], {n, 1, nmax}, {m, 0, 2^(n-1)}]] (* Jean-Fran├žois Alcover, Sep 28 2011 *)

CROSSREFS

Sequence in context: A131879 A172288 A134628 * A065158 A181842 A209564

Adjacent sequences:  A064879 A064880 A064881 * A064883 A064884 A064885

KEYWORD

nonn,easy,tabf

AUTHOR

Wolfdieter Lang, Oct 19 2001

STATUS

approved

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Last modified January 20 21:36 EST 2019. Contains 319336 sequences. (Running on oeis4.)