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A064885 Eisenstein array Ei(3,2). 1
3, 2, 3, 5, 2, 3, 8, 5, 7, 2, 3, 11, 8, 13, 5, 12, 7, 9, 2, 3, 14, 11, 19, 8, 21, 13, 18, 5, 17, 12, 19, 7, 16, 9, 11, 2, 3, 17, 14, 25, 11, 30, 19, 27, 8, 29, 21, 34, 13, 31, 18, 23, 5, 22, 17, 29, 12, 31, 19, 26, 7, 23, 16 (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=2; see pp. 41-2 of the Eisenstein reference given for A064881. The array for m=n=1 is A049456.

For n >= 1, the number of entries of row is 2^(n-1)+1 with the difference sequence [2,1,2,4,8,16,...]. Row sums give 5*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 3/2. The composition rule of this tree is i/j -> i/(i+j), (i+j)/j.

LINKS

Table of n, a(n) for n=1..63.

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)=2.

EXAMPLE

{3,2}; {3,5,2}; {3,8,5,7,2}; {3,11,8,13,5,12,7,9,2}; ...

This binary subtree of rationals is built from 3/2; 3/5,5/2; 3/8,8/5,5/7,7/2; ...

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

CROSSREFS

Sequence in context: A173093 A236361 A227634 * A029618 A264399 A240225

Adjacent sequences:  A064882 A064883 A064884 * A064886 A064887 A064888

KEYWORD

nonn,easy,tabf

AUTHOR

Wolfdieter Lang, Oct 19 2001

STATUS

approved

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Last modified January 17 05:26 EST 2019. Contains 319207 sequences. (Running on oeis4.)