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A000679
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Number of groups of order 2^n.
(Formerly M1470 N0581)
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22
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1, 1, 2, 5, 14, 51, 267, 2328, 56092, 10494213, 49487367289
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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REFERENCES
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James Gleick, Faster, Vintage Books, NY, 2000 (see pp. 259-261).
M. Hall, Jr. and J. K. Senior, The Groups of Order 2^n (n <= 6). Macmillan, NY, 1964.
M. F. Newman, Groups of prime-power order (1990). In Groups—Canberra 1989 (pp. 49-62). Springer, Berlin, Heidelberg. See Table 1.
M. F. Newman and E. A. O'Brien, A CAYLEY library for the groups of order dividing 128, Group theory (Singapore, 1987), 437-442, de Gruyter, Berlin-New York, 1989.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. Applebaum, J. Clikeman, J. A. Davis, J. F. Dillon, J. Jedwab, T. Rabbani, K. Smith, and W. Yolland, Constructions of difference sets in nonabelian 2-groups, Alg. Num. Theor. (2023) Vol. 17, No. 2. 359-396. See p. 396.
Bettina Eick and E. A. O'Brien, Enumerating p-groups. Group theory. J. Austral. Math. Soc. Ser. A 67 (1999), no. 2, 191-205.
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FORMULA
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a(n) = 2^((2/27)n^3 + O(n^(8/3))).
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EXAMPLE
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G.f. = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 51*x^5 + 267*x^6 + 2328*x^7 + ...
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MAPLE
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seq(GroupTheory:--NumGroups(2^n), n=0..10); # Robert Israel, Oct 15 2017
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,hard,more,nice
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AUTHOR
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EXTENSIONS
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a(9) and a(10) found by Eamonn O'Brien
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STATUS
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approved
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