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Search: id:A054247
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| A054247 |
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Number of n X n binary matrices under action of dihedral group of the square D_4. |
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+0
10
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| 1, 2, 6, 102, 8548, 4211744, 8590557312, 70368882591744, 2305843028004192256, 302231454921524358152192, 158456325028538104598816096256
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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(1/8)*(2^(n^2)+2*2^(n^2/4)+3*2^(n^2/2)+2*2^((n^2+n)/2)) if n is even and (1/8)*(2^(n^2)+2*2^((n^2+3)/4)+2^((n^2+1)/2)+4*2^((n^2+n)/2)) if n is odd.
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EXAMPLE
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There are 6 nonisomorphic 2 X 2 matrices under action of D_4:
[0 0] [0 0] [0 0] [0 1] [0 1] [1 1]
[0 0] [0 1] [1 1] [1 0] [1 1] [1 1].
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CROSSREFS
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Cf. A002724, A054407.
Sequence in context: A066091 A100704 A123257 this_sequence A099790 A059088 A057771
Adjacent sequences: A054244 A054245 A054246 this_sequence A054248 A054249 A054250
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), May 04 2000
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