

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
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OFFSET

1,1


COMMENTS

In Eisenstein's notation this is the array for m=3 and n=2; see pp. 412 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^(n1)+1 with the difference sequence [2,1,2,4,8,16,...]. Row sums give 5*A007051(n1).
The binary tree built from the rationals a(n,m)/a(n,m+1), m=0..2^(n1), for each row n >= 1 gives the subtree of the (Eisenstein)SternBrocot 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(n1, m/2) if m is even, else a(n, m)= a(n1, (m1)/2)+a(n1, (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)}]] (* JeanFrançois 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



