%I M4936 #45 Apr 13 2022 13:25:17

%S 2,14,86,518,3110,18662,111974,671846,4031078,24186470,145118822,

%T 870712934,5224277606,31345665638,188073993830,1128443962982,

%U 6770663777894,40623982667366,243743896004198,1462463376025190

%N Number of Boolean functions realized by cascades of n gates.

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

%H 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 J. T. Butler, <a href="/A005607/a005607_1.pdf">Letter to N. J. A. Sloane, Dec. 1978</a>.

%H 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 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992

%H <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-6)

%F a(n) = (2/5)*(6*6^(n-1) - 1). - _Ralf Stephan_, Apr 19 2004

%F a(n) = 6*a(n-1) + 2 for n > 1. - _Georg Fischer_, Nov 13 2018

%p 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 Table[(2/5) (6 6^(n - 1) - 1), {n, 1, 30}] (* _Bruno Berselli_, Nov 13 2018 *)

%Y Cf. A003464.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Ralf Stephan_, Apr 19 2004