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Search: id:A028365
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| A028365 |
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Order of general affine group over GF(2), AGL(n,2). |
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+0
2
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| 1, 2, 24, 1344, 322560, 319979520, 1290157424640, 20972799094947840, 1369104324918194995200, 358201502736997192984166400, 375234700595146883504949480652800, 1573079924978208093254925489963584716800
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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Putnam Exam. 1999, Question A6, Amer. Math. Monthly 107 (Oct 2000), 721-732; see p. 725.
J. M. Borwein, D. H. Bailey and R. Girgensohn, Experimentation in Mathematics, A K Peters, Ltd., Natick, MA, 2004. x+357 pp. See p. 54 (1.64).
I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.
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FORMULA
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a(n) = (6*a(n-1)^2*a(n-3) - 8*a(n-1)*a(n-2)^2) / (a(n-2)*a(n-3)). [From Putman Exam.] - Max Alekseyev (maxal(AT)cs.ucsd.edu), May 18 2007
a(n) is asymptotic to C*2^(n*(n+1)) where C=0.288788095086602421278899721...=prod(k>=1, 1-1/2^k) (cf. A048651) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 11 2003
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MAPLE
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A028365 := n->2^n*product(2^n-2^'i', 'i'=0..n-1); # version 1
A028365 := n->product(2^'j'-1, 'j'=1..n)*2^binomial(n+1, 2); # version 2
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PROGRAM
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(PARI) a(n)=if(n<0, 0, prod(k=1, n, 2^k-1)*2^((n^2+n)/2)) /* Michael Somos May 09 2005 */
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CROSSREFS
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Cf. A020522.
Sequence in context: A136524 A137887 A094050 this_sequence A000479 A111427 A081955
Adjacent sequences: A028362 A028363 A028364 this_sequence A028366 A028367 A028368
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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