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Search: id:A000722
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| A000722 |
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Invertible Boolean functions of n variables.
(Formerly M2144 N0853)
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+0
7
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| 1, 2, 24, 40320, 20922789888000, 263130836933693530167218012160000000, 12688693218588416410343338933516148080286551617454519219880189437521470423040000\ 0000000000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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These are invertible maps from {0,1}^n to {0,1}^n, or in other words permutations of the 2^n binary vectors of length n.
2^n-th order derivative of n-th Mandelbrot iterate. Example: a(2) = 24, after one iterate in the Mandelbrot(z(n+1) = z(n)^2 + c) we have the function z(2) = z^4 + 2*c*z^2 + c^2 + c, for which the 4-th order derivative is 24. - Bert van den Bosch (zeusooooo(AT)hotmail.com), Sep 07 2003
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541.
I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.
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LINKS
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Index entries for sequences related to Boolean functions
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FORMULA
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a(n) = (2^n)!.
Sum of reciprocals = 0.54169146825401604874... - Cino Hilliard (hillcino368(AT)gmail.com), Feb 08 2003
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PROGRAM
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(PARI) atonfact(a, n) = {sr=0; for(x=1, n, y =(a^x)!; sr+=1.0/y; print1(y" "); ); print(); print(sr) }
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CROSSREFS
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Cf. A001038 A000653 A000654 A000652 A001537 A046856 A046857
Sequence in context: A062716 A137888 A108349 this_sequence A098679 A123851 A120122
Adjacent sequences: A000719 A000720 A000721 this_sequence A000723 A000724 A000725
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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