A005610 Number of Boolean functions realized by cascades of n gates. (Formerly M4936)

2, 14, 86, 518, 3110, 18662, 111974, 671846, 4031078, 24186470, 145118822, 870712934, 5224277606, 31345665638, 188073993830, 1128443962982, 6770663777894, 40623982667366, 243743896004198, 1462463376025190

Offset

1,1

References

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

Links

Table of n, a(n) for n=1..20.

J. T. Butler, Fanout-free networks of multivalued gates, Proc. Internat. Symposium Multiple-Valued Logic, Charlotte, NC, 1977, IEEE Press, NY (1977), 39-46. (Annotated scanned copy)

J. T. Butler, Letter to N. J. A. Sloane, Dec. 1978.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Index entries for sequences related to Boolean functions

Index entries for linear recurrences with constant coefficients, signature (7,-6)

Formula

a(n) = (2/5)*(6*6^(n-1) - 1). - Ralf Stephan, Apr 19 2004

a(n) = 6*a(n-1) + 2 for n > 1. - Georg Fischer, Nov 13 2018

Maple

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

Mathematica

Table[(2/5) (6 6^(n - 1) - 1), {n, 1, 30}] (* Bruno Berselli, Nov 13 2018 *)

Crossrefs

Cf. A003464.

Sequence in context: A036692 A075140 A037563 * A065355 A162478 A348615

Adjacent sequences: A005607 A005608 A005609 * A005611 A005612 A005613

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Ralf Stephan, Apr 19 2004

Status

approved