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Search: id:A060710
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| A060710 |
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Number of subgroups of dihedral group with 2n elements, counting conjugate subgroups only once, i.e. conjugacy classes of subgroups of the dihedral group. |
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+0
4
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| 2, 5, 4, 8, 4, 10, 4, 11, 6, 10, 4, 16, 4, 10, 8, 14, 4, 15, 4, 16, 8, 10, 4, 22, 6, 10, 8, 16, 4, 20, 4, 17, 8, 10, 8, 24, 4, 10, 8, 22, 4, 20, 4, 16, 12, 10, 4, 28, 6, 15, 8, 16, 4, 20, 8, 22, 8, 10, 4, 32, 4, 10, 12, 20, 8, 20, 4, 16, 8, 20, 4, 33, 4, 10, 12, 16, 8, 20, 4, 28, 10, 10, 4
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The total number of subgroups, counting conjugate subgroups as distinct, is A007503.
Also the number of subgroups of the group C_nxC_2 (where C_n is the cyclic group with n elements).
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
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For odd n: a(n) = tau(2n) = 2*tau(n)= 2*A000005(n). - Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 12 2001
For even n, a(n) = 2*tau(n)+tau(n/2).
Moebius transform is period 2 sequence [2, 3, ...]. - Michael Somos Sep 20 2005
G.f.: Sum_{k>0} x^k(2+3x^k)/(1-x^(2k)) = Sum_{k>0} 2*x^(2k-1)/(1-x^(2k-1))+3*x^(2k)/(1-x^(2k)) . - Michael Somos Sep 20 2005
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EXAMPLE
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The dihedral group D6 is isomorphic to the symmetric group S_3 and the conjugacy classes of subgroups are: the trivial group, the whole group, subgroup of order 2 generated by a transposition and the subgroup A_3 generated by the 3-cycles. So a(3) = 4.
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PROGRAM
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(PARI) a(n)=if(n<1, 0, sumdiv(n, d, 3-d%2)) /* Michael Somos Sep 20 2005 */
(PARI) { for (n=1, 1000, write("b060710.txt", n, " ", sumdiv(n, d, 3 - d%2)); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 10 2009]
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CROSSREFS
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Cf. A007503, A062011.
Sequence in context: A111570 A057954 A155896 this_sequence A146101 A093052 A081556
Adjacent sequences: A060707 A060708 A060709 this_sequence A060711 A060712 A060713
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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 21 2001
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 15 2001
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