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A060632
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2^wt(floor(n/2)) (i.e. 2^A000120([n/2]), or A001316([n/2])).
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13
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of conjugacy classes in the symmetric group S_n that have odd number of elements.
Also sequence A001316 doubled.
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
First differences of A151566. Sequence gives number of toothpicks added at the n-th generation of the leftist toothpick sequence A151566.
The Fi1 and Fi1 triangle sums, see A180662 for their definitions, of Sierpinski’s triangle A047999 equal this sequence. [From Johannes W. Meijer, Jun 05 2011]
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REFERENCES
| I. G. MacDonald: Symmetric functions and Hall polynomials Oxford: Clarendon Press, 1979. Page 21.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,1000
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Index entries for sequences related to toothpick sequences
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FORMULA
| 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
a(n) = gcd(A056040(n), 2^n) - Peter Luschny, Jun 30 2011
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EXAMPLE
| 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).
Contribution from Omar E. Pol, Oct 12 2011 (Start):
Written as a triangle:
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,...
(End)
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MAPLE
| A060632 := proc(n) local k; add(binomial(n, 2*k) mod 2, k=0..floor(n/2)); end: seq(A060632(n), n=0..94);
[From Peter Luschny, Jun 30 2011](Start)
A060632 := n -> 2^add(i, i = convert(iquo(n, 2), base, 2));
A060632 := n -> igcd(2^n, n! / iquo(n, 2)!^2); # (End)
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PROG
| (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]
(MAGMA) a000120:=func< n | &+Intseq(n, 2) >; [ 2^a000120(Floor(n/2)): n in [0..100] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 15 2010]
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CROSSREFS
| Cf. A000120, A001316.
Cf. A139251, A151566, A160407. [From Omar E. Pol (info(AT)polprimos.com), Jun 12 2009]
Sequence in context: A122386 A051464 A151565 * A160407 A007457 A119802
Adjacent sequences: A060629 A060630 A060631 * A060633 A060634 A060635
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KEYWORD
| nonn
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AUTHOR
| Avi Peretz (njk(AT)netvision.net.il), Apr 15 2001
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EXTENSIONS
| 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; Oct 11 2010
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
Maple program edited by Johannes W. Meijer, May 28 2011
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