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Search: id:A063073
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| A063073 |
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Square of determinant of character table of the dihedral group with 2n elements. |
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+0
2
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| 4, 256, 36, 4096, 500, 82944, 9604, 2097152, 236196, 64000000, 7086244, 2293235712, 250994068, 94450499584, 10251562500, 4398046511104, 474351505988, 228509902503936, 24524265031204, 13107200000000000
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For any finite group G with order n we have that if A is the character table then |det(A)|^2 = product i (n/c(i)) where the product is over the conjugacy classes of G: c(i), so by this formula the square of the determinant is an integer (in the case of dihedral groups the characters are real).
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,200
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FORMULA
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a(n) = 4 * n^((n+1)/2) if n odd, a(n)= 64 * n^((n+2)/2) if n even. - Paul Boddington (psb(AT)maths.warwick.ac.uk), Oct 22 2003
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PROGRAM
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(PARI) { for (n=1, 200, if (n%2, a=4 * n^((n+1)/2), a=64 * n^((n+2)/2)); write("b063073.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 16 2009]
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CROSSREFS
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Sequence in context: A091792 A090602 A087587 this_sequence A093760 A062075 A013734
Adjacent sequences: A063070 A063071 A063072 this_sequence A063074 A063075 A063076
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KEYWORD
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nonn
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AUTHOR
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Ahmed Fares (ahmedfares(AT)my-deja.com), Aug 03 2001
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EXTENSIONS
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Missing term included and more terms added by Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 16 2009
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