%I A060632
%S A060632 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,
%T A060632 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,
%U A060632 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
%N A060632 2^wt(floor(n/2)) (i.e. 2^A000120([n/2]), or A001316([n/2])).
%C A060632 Number of conjugacy classes in the symmetric group S_n that have odd 
               number of elements.
%C A060632 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
%C A060632 Apart from the first element, this is also sequence A001316 doubled.
%D A060632 I. G. MacDonald: Symmetric functions and Hall polynomials Oxford: Clarendon 
               Press, 1979. Page 21.
%H A060632 Harry J. Smith, <a href="b060632.txt">Table of n, a(n) for n=0,...,1000</
               a>
%F A060632 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
%e A060632 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).
%p A060632 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:
%o A060632 (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]
%Y A060632 Cf. A000120, A001316.
%Y A060632 Sequence in context: A125913 A122386 A051464 this_sequence A151565 A160407 
               A007457
%Y A060632 Adjacent sequences: A060629 A060630 A060631 this_sequence A060633 A060634 
               A060635
%K A060632 nonn
%O A060632 0,3
%A A060632 Avi Peretz (njk(AT)netvision.net.il), Apr 15 2001
%E A060632 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 16 2001
%E A060632 Edited by N. J. A. Sloane (njas(AT)research.att.com), Jun 06 2008
%E A060632 a(0) = 1 added by N. J. A. Sloane (njas(AT)research.att.com), Sep 14 
               2009
%E A060632 FORMULA corrected by Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 
               15 2009