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A053722
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Number of n X n binary matrices of order dividing 2 (also number of solutions to X^2=I in GL(n,2)).
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23
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1, 4, 22, 316, 6976, 373024, 32252032, 6619979776, 2253838544896, 1810098020122624, 2442718932612677632, 7758088894129169760256, 41674675294431186817908736, 526370120583359572695165435904
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OFFSET
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1,2
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COMMENTS
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In characteristic 2, A^2 = I if and only if B^2 = 0 where B = I + A, so a(n) is also equal to the number of n X n binary matrices B such that B^2 = 0.
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REFERENCES
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V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
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LINKS
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Table of n, a(n) for n=1..14.
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FORMULA
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a(n) = sum k=1...[n/2] (2^n - 1)(2^n - 2) ... (2^n - 2^{n-k+1})/(2^k - 1)(2^k - 2)....(2^k - 2^{k-1}) * (2^{n-k} - 1)(2^{n-k} - 2)...(2^{n-k} - 2^{n-2k+1}). - Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 05 2001
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CROSSREFS
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Sequence in context: A125801 A195227 A119009 * A145504 A104166 A065401
Adjacent sequences: A053719 A053720 A053721 * A053723 A053724 A053725
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KEYWORD
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nonn,changed
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AUTHOR
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Vladeta Jovovic, Mar 23 2000
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STATUS
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approved
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