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A064886 Eisenstein array Ei(2,3). 4
2, 3, 2, 5, 3, 2, 7, 5, 8, 3, 2, 9, 7, 12, 5, 13, 8, 11, 3, 2, 11, 9, 16, 7, 19, 12, 17, 5, 18, 13, 21, 8, 19, 11, 14, 3, 2, 13, 11, 20, 9, 25, 16, 23, 7, 26, 19, 31, 12, 29, 17, 22, 5, 23, 18, 31, 13, 34, 21, 29, 8, 27, 19, 30 (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=3; see pp. 41-2 of the Eisenstein reference given for A064881. This is identical with the array for m=3,n=2, given in A064885, read backwards. The array for m=n=1 is A049456.

For n >= 1, the number of entries of row n >= 1 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 2/3. The composition rule of this tree is i/j -> i/(i+j), (i+j)/j.

LINKS

Table of n, a(n) for n=1..64.

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)=3.

EXAMPLE

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

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

MATHEMATICA

a[1, 0] = 2; a[1, 1] = 3; a[n_ /; n >= 1, m_ /; m >= 0] := If[EvenQ[m], a[n, m] = a[n-1, m/2], a[n, m] = a[n-1, (m-1)/2] + a[n-1, (m+1)/2]]; Table[a[n, m], {n, 1, 6}, {m, 0, 2^(n-1)}] // Flatten (* Jean-Fran├žois Alcover, Feb 27 2018 *)

CROSSREFS

Sequence in context: A302170 A049805 A104887 * A029600 A169616 A111076

Adjacent sequences:  A064883 A064884 A064885 * A064887 A064888 A064889

KEYWORD

nonn,easy,tabf

AUTHOR

Wolfdieter Lang, Oct 19 2001

STATUS

approved

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Last modified January 18 16:40 EST 2019. Contains 319271 sequences. (Running on oeis4.)