cp's OEIS Frontend

A005610 Number of Boolean functions realized by cascades of n gates.

%I A005610 M4936 #45 Apr 13 2022 13:25:17
%S A005610 2,14,86,518,3110,18662,111974,671846,4031078,24186470,145118822,
%T A005610 870712934,5224277606,31345665638,188073993830,1128443962982,
%U A005610 6770663777894,40623982667366,243743896004198,1462463376025190
%N A005610 Number of Boolean functions realized by cascades of n gates.
%D A005610 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005610 J. T. Butler, <a href="/A005607/a005607.pdf">Fanout-free networks of multivalued gates</a>, Proc. Internat. Symposium Multiple-Valued Logic, Charlotte, NC, 1977, IEEE Press, NY (1977), 39-46. (Annotated scanned copy)
%H A005610 J. T. Butler, <a href="/A005607/a005607_1.pdf">Letter to N. J. A. Sloane, Dec. 1978</a>.
%H A005610 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H A005610 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H A005610 <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>
%H A005610 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-6)
%F A005610 a(n) = (2/5)*(6*6^(n-1) - 1). - _Ralf Stephan_, Apr 19 2004
%F A005610 a(n) = 6*a(n-1) + 2 for n > 1. - _Georg Fischer_, Nov 13 2018
%p A005610 A005610:=-2*(-7+6*z)/(6*z-1)/(z-1); # conjectured by _Simon Plouffe_ in his 1992 dissertation; gives the sequence apart from the initial 2
%t A005610 Table[(2/5) (6 6^(n - 1) - 1), {n, 1, 30}] (* _Bruno Berselli_, Nov 13 2018 *)
%Y A005610 Cf. A003464.
%K A005610 nonn,easy
%O A005610 1,1
%A A005610 _N. J. A. Sloane_
%E A005610 More terms from _Ralf Stephan_, Apr 19 2004