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Search: id:A136184
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| A136184 |
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Number of metacyclic groups of order 2^n. |
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+0
2
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| 1, 2, 4, 8, 12, 19, 26, 37, 48, 63, 78, 98, 117, 142, 166, 196, 225, 261, 295, 337, 377, 425, 471, 526, 578, 640, 699, 768, 834, 911, 984, 1069, 1150, 1243, 1332, 1434, 1531, 1642, 1748, 1868, 1983, 2113, 2237, 2377, 2511, 2661, 2805, 2966, 3120, 3292, 3457
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For number of metacyclic groups of order p^n, prime p >= 3, see A136185.
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LINKS
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K. Brockhaus, Table of n, a(n) for n=1..1000 [Values computed with MAGMA]
MAGMA Computational Algebra System, V2.14-1, Metacyclic p-groups
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FORMULA
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G.f. (conjectured): -x*(x^10 + x^9 - x^8 + x^6 - x^3 - x - 1)/((x - 1)^4*(x + 1)^2*(x^2 + x + 1)).
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EXAMPLE
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a(3) = 4 since there are four metacyclic groups of order 2^3; they have invariants <3, 0, 0, 3, [ 8 ], >, <1, 2, 1, 1, [ 2, 4 ], >, <1, 1, 1, 2, [ 2 ], Dihedral> and <1, 1, 1, 2, [ 2 ], Quaternion> resp. (for details see MAGMA link).
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PROGRAM
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(MAGMA) [ NumberOfMetacyclicPGroups(2, n): n in [1..51] ];
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CROSSREFS
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Cf. A136185.
Adjacent sequences: A136181 A136182 A136183 this_sequence A136185 A136186 A136187
Sequence in context: A006500 A134181 A125606 this_sequence A011908 A117455 A110571
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 19 2007
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