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Search: id:A028666
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| A028666 |
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a(n) = order of the orthogonal group O_n(2) if n is odd or O^(+)_n(2) if n is even. |
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+0
3
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| 1, 1, 12, 2880, 11612160, 758041804800, 794088208701849600, 13319336815141167562752000, 3575164027575627746190393606144000, 15354978274323252140217954794120612413440000, 1055182047088717407398960909148529544369642384916480000, 1160183823755957350394353874696058298158177597536388268425216000000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Pseudo-Galois numbers for d=4; order of group AGL(n,2^2).
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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, p. xii (but beware typos!).
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FORMULA
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a(n) = p^n Product (p^n - p^k) for k=0 to n-1
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MAPLE
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f:=proc(n, eps) local m, d;
if n mod 2 = 0 then m:=n/2; d:=gcd(4, 2^m-eps);
2^(m*(m-1))*mul( 4^i-1, i=1..m)*(2^m-eps)/d;
else m:=(n-1)/2;
2^(m^2)*mul( 4^i-1, i=1..m);
fi; end;
[seq(f(n, +1), n=0..20)]
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MATHEMATICA
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FoldList[ #1*4^#2 (4^#2-1)&, 1, Range[ 20 ] ]
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CROSSREFS
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Bisections give A144546 and A144547.
Sequence in context: A092299 A006272 A111237 this_sequence A103658 A012603 A012737
Adjacent sequences: A028663 A028664 A028665 this_sequence A028667 A028668 A028669
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KEYWORD
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nonn
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
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Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Dec 30 2008
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