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A064884
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Eisenstein array Ei(3,1).
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| In Eisenstein's notation this is the array for m=3 and n=1; see pp. 41-2 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^(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 3/1. The composition rule of this tree is i/j -> i/(i+j), (i+j)/j.
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LINKS
| Index entries for sequences related to Stern's sequences
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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)=1.
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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; ...
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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] = 1; Flatten[Table[a[n, m], {n, 1, nmax}, {m, 0, 2^(n-1)}]] (* From Jean-François Alcover, Sep 28 2011 *)
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CROSSREFS
| Sequence in context: A076152 A107638 A104765 * A093560 A173934 A131504
Adjacent sequences: A064881 A064882 A064883 * A064885 A064886 A064887
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KEYWORD
| nonn,easy,tabf
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 19 2001
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