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A064883 Eisenstein array Ei(1,3). 1
1, 3, 1, 4, 3, 1, 5, 4, 7, 3, 1, 6, 5, 9, 4, 11, 7, 10, 3, 1, 7, 6, 11, 5, 14, 9, 13, 4, 15, 11, 18, 7, 17, 10, 13, 3, 1, 8, 7, 13, 6, 17, 11, 16, 5, 19, 14, 23, 9, 22, 13, 17, 4, 19, 15, 26, 11, 29, 18, 25, 7, 24, 17, 27, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In Eisenstein's notation this is the array for m=1 and n=3; 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 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 1/3. The composition rule for this tree is i/j -> i/(i+j), (i+j)/j.

LINKS

Table of n, a(n) for n=1..65.

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

EXAMPLE

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

This binary subtree of rationals is built from 1/3; 1/4,4/3; 1/5,5/4,4/7,7/3; ...

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] = 1; a[1, 1] = 3; Flatten[ Table[ a[n, m], {n, 1, nmax}, {m, 0, 2^(n-1)}]] (* Jean-Fran├žois Alcover, Oct 03 2011 *)

CROSSREFS

Sequence in context: A191818 A055171 A101038 * A090844 A008314 A104568

Adjacent sequences:  A064880 A064881 A064882 * A064884 A064885 A064886

KEYWORD

nonn,easy,tabf

AUTHOR

Wolfdieter Lang, Oct 19 2001

STATUS

approved

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Last modified January 21 20:00 EST 2019. Contains 319350 sequences. (Running on oeis4.)