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A000722 Invertible Boolean functions of n variables.
(Formerly M2144 N0853)
7
1, 2, 24, 40320, 20922789888000, 263130836933693530167218012160000000, 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000 (list; graph; refs; listen; history; internal format)
OFFSET

0,2

COMMENTS

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

REFERENCES

C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.

LINKS

Index entries for sequences related to Boolean functions

FORMULA

a(n) = (2^n)!.

Sum of reciprocals = 0.54169146825401604874... - Cino Hilliard (hillcino368(AT)gmail.com), Feb 08 2003

PROG

(PARI) atonfact(a, n) = {sr=0; for(x=1, n, y =(a^x)!; sr+=1.0/y; print1(y" "); ); print(); print(sr) }

CROSSREFS

Cf. A001038 A000653 A000654 A000652 A001537 A046856 A046857

Sequence in context: A062716 A137888 A108349 * A098679 A123851 A120122

Adjacent sequences:  A000719 A000720 A000721 * A000723 A000724 A000725

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified February 17 11:35 EST 2012. Contains 206011 sequences.