A000679 - OEIS (original) (raw)

REFERENCES

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).

LINKS

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.

Hans Ulrich Besche and Bettina Eick, Construction of finite groups, Journal of Symbolic Computation, Vol. 27, No. 4, Apr 15 1999, pp. 387-404.

Hans Ulrich Besche, Bettina Eick and E. A. O'Brien, The groups of order at most 2000, Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 1-4.

Bettina Eick and E. A. O'Brien, Enumerating p-groups. Group theory. J. Austral. Math. Soc. Ser. A 67 (1999), no. 2, 191-205.

Rodney James, M. F. Newman, and E. A. O'Brien, The Groups of Order 128, J. Algebra 129, 136-158, 1990.

Eric Weisstein's World of Mathematics, Finite Group.

FORMULA

a(n) = 2^((2/27)n^3 + O(n^(8/3))).

EXAMPLE

G.f. = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 51*x^5 + 267*x^6 + 2328*x^7 + ...

MAPLE

seq(GroupTheory:--NumGroups(2^n), n=0..10); # Robert Israel, Oct 15 2017

MATHEMATICA

Join[{1}, FiniteGroupCount[2^Range[10]]] (* Vincenzo Librandi, Mar 28 2018 *)

EXTENSIONS

a(9) and a(10) found by Eamonn O'Brien