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A005609 Number of Boolean functions realized by cascades of n gates.
(Formerly M5333)
3
64, 1744, 48784, 1365904, 38245264, 1070867344, 29984285584, 839559996304, 23507679896464, 658215037100944, 18430021038826384, 516040589087138704, 14449136494439883664, 404575821844316742544, 11328123011640868791184 (list; graph; refs; listen; history; text; internal format)
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..15.

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 (29, -28).

FORMULA

G.f.: (64 - 112 x) / (1 - x) (1 - 28 x).

a(1)=64, a(2)=1744, a(n) = 29*a(n-1) - 28*a(n-2). - Harvey P. Dale, Nov 19 2011

a(n) = N(n,2,3) where N(n,s,r) is defined in A005608. - Sean A. Irvine, Jul 13 2016

MAPLE

A005609:=-16*(-4+7*z)/(28*z-1)/(z-1); # conjectured by Simon Plouffe in his 1992 dissertation

MATHEMATICA

CoefficientList[Series[(64-112 x)/((1-x) (1-28 x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{29, -28}, {64, 1744}, 30] (* Harvey P. Dale, Nov 19 2011 *)

CROSSREFS

Cf. A005608, A005618.

Sequence in context: A234240 A017115 A269203 * A065788 A264275 A283689

Adjacent sequences:  A005606 A005607 A005608 * A005610 A005611 A005612

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 25 12:11 EDT 2019. Contains 321470 sequences. (Running on oeis4.)