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A005610
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Number of Boolean functions realized by cascades of n gates.
(Formerly M4936)
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3
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2, 14, 86, 518, 3110, 18662, 111974, 671846, 4031078, 24186470, 145118822, 870712934, 5224277606, 31345665638, 188073993830, 1128443962982, 6770663777894, 40623982667366, 243743896004198, 1462463376025190
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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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.
Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.
Index entries for sequences related to Boolean functions
Index entries for linear recurrences with constant coefficients, signature (7,-6)
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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Table[(2/5) (6 6^(n - 1) - 1), {n, 1, 30}] (* Bruno Berselli, Nov 13 2018 *)
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CROSSREFS
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Cf. A003464.
Sequence in context: A036692 A075140 A037563 * A065355 A162478 A189392
Adjacent sequences: A005607 A005608 A005609 * A005611 A005612 A005613
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Ralf Stephan, Apr 19 2004
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STATUS
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approved
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