

A064884


Eisenstein array Ei(3,1).


0



3, 1, 3, 4, 1, 3, 7, 4, 5, 1, 3, 10, 7, 11, 4, 9, 5, 6, 1, 3, 13, 10, 17, 7, 18, 11, 15, 4, 13, 9, 14, 5, 11, 6, 7, 1, 3, 16, 13, 23, 10, 27, 17, 24, 7, 25, 18, 29, 11, 26, 15, 19, 4, 17, 13, 22, 9, 23, 14, 19, 5, 16, 11, 17, 6, 13
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OFFSET

1,1


COMMENTS

In Eisenstein's notation this is the array for m=3 and n=1; see pp. 4142 of the Eisenstein reference given for A064881. This is identical with the array for m=1,n=3, given in A064883, read backwards. The array for m=n=1 is A049456.
For n >= 1, the number of entries of row n is 2^(n1)+1 with the difference sequence [2,1,2,4,8,16,...]. Row sums give 4*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 3/1. The composition rule of this tree is i/j > i/(i+j), (i+j)/j.


LINKS

Table of n, a(n) for n=1..66.
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)=1.


EXAMPLE

{3,1};
{3,4,1};
{3,7,4,5,1};
{3,10,7,11,4,9,5,6,1}; ...
This binary subtree of rationals is built from
3/1;
3/4,4/1;
3/7,7/4,4/5,5/1; ...


MATHEMATICA

nmax = 6; a[n_, m_?EvenQ] := a[n1, m/2]; a[n_, m_?OddQ] := a[n, m] = a[n1, (m1)/2] + a[n1, (m+1)/2]; a[1, 0] = 3; a[1, 1] = 1; Flatten[Table[a[n, m], {n, 1, nmax}, {m, 0, 2^(n1)}]] (* JeanFrançois Alcover, Sep 28 2011 *)
eisen = Most@Flatten@Transpose[{#, # + RotateLeft[#]}] &;
Flatten@NestList[eisen, {3, 1}, 6] (* Harlan J. Brothers, Feb 18 2015 *)


CROSSREFS

Sequence in context: A107638 A245093 A104765 * A093560 A173934 A131504
Adjacent sequences: A064881 A064882 A064883 * A064885 A064886 A064887


KEYWORD

nonn,easy,tabf


AUTHOR

Wolfdieter Lang, Oct 19 2001


STATUS

approved



