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Search: id:A063505
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| A063505 |
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Number of n X n upper triangular binary matrices over GF(2) B such that B^2 = 0. |
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+0
1
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| 2, 8, 32, 320, 2592, 57472, 946176, 44302336, 1482686464, 143210315776, 9732400087040, 1915349322694656, 263918421714927616, 105091512697853313024, 29316605112733216538624, 23522116026027393322844160
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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In the reference a more general formula is given for the number of such matrices over GF(q) for any q.
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REFERENCES
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Shalosh B. Ekhad, Doron Zeilberger, An Explicit Formula for the Number of Solutions of X^2=0 in Triangular Matrices over a Finite Field. Elec. J. Comb. 3(1)(1996)
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LINKS
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Shalosh B. Ekhad, Doron Zeilberger, [math/9512224] An Explicit Formula for the Number of Solutions of X^2=0 in Triangular Matrices over a Finite Field, Elec. J. Comb. 3(1)(1996)
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FORMULA
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a(2n) = sum j (C(2n, n - 3j) - C(2n, n - 3j - 1)) * 2^(n^2 - 3j^2 - j) a(2n+1) = sum j (C(2n + 1, n - 3j) - C(2n + 1, n - 3j - 1)) * 2^(n^2 + n - 3j^2 - 2j)
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CROSSREFS
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A053722.
Adjacent sequences: A063502 A063503 A063504 this_sequence A063506 A063507 A063508
Sequence in context: A062797 A134751 A139014 this_sequence A085466 A084039 A135620
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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), Jul 30 2001
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 01 2001
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