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Search: id:A060632
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| 1, 1, 2, 2, 2, 2, 4, 4, 2, 2, 4, 4, 4, 4, 8, 8, 2, 2, 4, 4, 4, 4, 8, 8, 4, 4, 8, 8, 8, 8, 16, 16, 2, 2, 4, 4, 4, 4, 8, 8, 4, 4, 8, 8, 8, 8, 16, 16, 4, 4, 8, 8, 8, 8, 16, 16, 8, 8, 16, 16, 16, 16, 32, 32, 2, 2, 4, 4, 4, 4, 8, 8, 4, 4, 8, 8, 8, 8, 16, 16, 4, 4, 8, 8, 8, 8, 16, 16, 8, 8, 16, 16, 16, 16, 32
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of conjugacy classes in the symmetric group S_n that have odd number of elements.
Number of even numbers whose binary expansion is a child of the binary expansion of n. - Nadia Heninger and N. J. A. Sloane (njas(AT)research.att.com), Jun 06 2008
Apart from the first element, this is also sequence A001316 doubled.
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REFERENCES
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I. G. MacDonald: Symmetric functions and Hall polynomials Oxford: Clarendon Press, 1979. Page 21.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,1000
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FORMULA
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a(n)=sum{k=0..floor(n/2), C(n, 2k) mod 2} - Paul Barry (pbarry(AT)wit.ie), Jan 03 2005, Edited by Harry J. Smith, Sep 15 2009
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EXAMPLE
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a(3) = 2 because in S_3 there are two conjugacy classes with odd number of elements, the trivial conjugacy class and the conjugacy class of transpositions consisting of 3 elements: (12),(13),(23).
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MAPLE
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A001316 := proc(n) local k; add(binomial(n, k) mod 2, k=0..n); end: for n from 1 to 250 do printf(`%d, `, A001316(floor(n/2))) od:
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PROGRAM
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(PARI) { for (n=0, 1000, write("b060632.txt", n, " ", sum(k=0, floor(n/2), binomial(n, 2*k) % 2)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 14 2009]
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CROSSREFS
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Cf. A000120, A001316.
Sequence in context: A125913 A122386 A051464 this_sequence A151565 A160407 A007457
Adjacent sequences: A060629 A060630 A060631 this_sequence A060633 A060634 A060635
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KEYWORD
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nonn
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AUTHOR
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Avi Peretz (njk(AT)netvision.net.il), Apr 15 2001
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 16 2001
Edited by N. J. A. Sloane (njas(AT)research.att.com), Jun 06 2008
a(0) = 1 added by N. J. A. Sloane (njas(AT)research.att.com), Sep 14 2009
FORMULA corrected by Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 15 2009
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