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

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

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

Links

• 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)

Crossrefs

Cf. A003464.

Programs

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 *)

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

Extensions

More terms from Ralf Stephan, Apr 19 2004