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%I M2173 N0868 #38 Feb 12 2021 18:16:50
%S 1,2,52,142090700,17844701940501123640681816160,
%T 59757436204078657410908164193971330396709572693816353610758085074676243846093824
%N Invertible Boolean functions of n variables.
%C Equivalence classes of invertible maps from {0,1}^n to {0,1}^n, under action of permutation and complementation of variables on domain and range. - _Sean A. Irvine_, Mar 16 2011
%D M. A. Harrison, The number of classes of invertible Boolean functions, J. ACM 10 (1963), 25-28.
%D C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Adam P. Goucher, <a href="/A000654/b000654.txt">Table of n, a(n) for n = 1..7</a>
%H M. A. Harrison, <a href="/A000653/a000653.pdf">The number of classes of invertible Boolean functions</a>, J. ACM 10 (1963), 25-28. [Annotated scan of page 27 only]
%H M. A. Harrison, <a href="/A000370/a000370.pdf">The number of equivalence classes of Boolean functions under groups containing negation</a>, IEEE Trans. Electron. Comput. 12 (1963), 559-561. [Annotated scanned copy]
%H C. S. Lorens, <a href="http://dx.doi.org/10.1109/PGEC.1964.263724">Invertible Boolean functions</a>, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541.
%H C. S. Lorens, <a href="/A000722/a000722.pdf">Invertible Boolean functions</a>, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541. [Annotated scan of page 530 only]
%H Qing-bin Luo, Jin-zhao Wu, Chen Lin, <a href="https://doi.org/10.1007/s10773-020-04508-y">Computing the Number of the Equivalence Classes for Reversible Logic Functions</a>, Int'l J. of Theor. Phys. (2020) Vol. 59, 2384-2396.
%H <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>
%t cyclify =
%t Function[{x},
%t Sort@Tally[Length /@ PermutationCycles[x + 1, Identity]]];
%t totalweight =
%t Function[{c}, Product[(x[[1]]^x[[2]]) ( x[[2]]!), {x, c}]];
%t perms = Function[{n},
%t Flatten[Table[
%t FromDigits[Permute[IntegerDigits[BitXor[x, a], 2, n], sigma],
%t 2], {sigma, Permutations[Range[n]]}, {a, 0, 2^n - 1}, {x, 0,
%t 2^n - 1}], 1]];
%t countit =
%t Function[{n},
%t Sum[totalweight[x[[1]]] (x[[2]]^2), {x,
%t Tally[cyclify /@ perms[n]]}]/((2^n) (n!))^2];
%t Table[countit[n], {n, 1, 5}] (* _Adam P. Goucher_, Feb 12 2021 *)
%K nonn
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Mar 15 2011
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