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A070953
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Order of the group GU(n,2), the general unitary n X n matrices over the finite field GF(4).
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0
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3, 18, 648, 77760, 41057280, 82771476480, 683361309818880, 22304913152488243200, 2929259634489976002969600, 1534275894314621670931405209600, 3219180858829475639028172057057689600
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OFFSET
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1,1
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COMMENTS
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Replacing 2 in the definition by a prime power q, the order of the group GU(n,q), the general unitary n X n matrices over the finite field GF(q^2) is (q+1) * q^(n(n-1)/2) * product i=1..(n-1) (q^(i+1) - (-1)^(i+1)).
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REFERENCES
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J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups, Oxford Univ. Press, 1985.
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LINKS
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FORMULA
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For n>=2 a(n) = 3 * 2^(n(n-1)/2) * product i=1..(n-1) (2^(i+1) - (-1)^(i+1))
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MATHEMATICA
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Table[3*2^(n*(n-1)/2) * Product[2^(k+1) - (-1)^(k+1), {k, 1, n-1}], {n, 1, 12}]
(* or *) Table[I^(n*(n+3)) * 2^((n-1)*n/2) * QPochhammer[-2, -2, n], {n, 1, 12}] (* Vaclav Kotesovec, Jan 06 2021 *)
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PROG
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(PARI) for(n=2, 30, print1( 3*2^(n*(n-1)/2)*prod(i=1, (n-1), (2^(i+1)-(-1)^(i+1))), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Sharon Sela (sharonsela(AT)hotmail.com), May 24 2002
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EXTENSIONS
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STATUS
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approved
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