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Search: id:A064885
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| A064885 |
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Eisenstein array Ei(3,2). |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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In Eisenstein's notation this is the array for m=3 and n=2; 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 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 3/2. The composition rule of this tree is i/j -> i/(i+j), (i+j)/j.
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LINKS
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Index entries for sequences related to Stern's sequences
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FORMULA
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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)=2.
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EXAMPLE
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{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; ...
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CROSSREFS
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Sequence in context: A091821 A086035 A003559 this_sequence A029618 A112427 A098229
Adjacent sequences: A064882 A064883 A064884 this_sequence A064886 A064887 A064888
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 19 2001
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