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A005619 Number of Boolean functions realized by n-input cascades.
(Formerly M5020)
1
16, 240, 6448, 187184, 5474096, 160196400, 4688357168, 137211717424, 4015706384176, 117525666899760, 3439564830058288, 100664021209884464, 2946083492311639856, 86221550057181718320, 2523402922444883797808, 73851169513661744064304 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

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=2..17.

J. T. Butler, Tandem networks of universal cells, IEEE Trans. Computers, C-27 (1978), 785-799. (Annotated scanned copy)

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

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

Index entries for sequences related to Boolean functions

FORMULA

a(n) = C1 * alpha1^(n+1) + C2 * alpha2^(n+1) + 48/49 where C1 = (-1202 + 363*s) / (1960*s), C2 = (1202 + 363*s) / (1960*s), alpha1 = 16 + 4*s, alpha2 = 16 - 4*s, s=sqrt(11) [From Butler]. - Sean A. Irvine, Jul 20 2016

MAPLE

A005619:= -16*z^2*(1-18*z+20*z^2)/((z-1)*(80*z^2-32*z+1)); # conjectured by Simon Plouffe in his 1992 dissertation

CROSSREFS

Sequence in context: A170697 A170735 A058667 * A204793 A173605 A175720

Adjacent sequences:  A005616 A005617 A005618 * A005620 A005621 A005622

KEYWORD

nonn,changed

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Sean A. Irvine, Jul 20 2016

STATUS

approved

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Last modified February 27 11:38 EST 2021. Contains 341656 sequences. (Running on oeis4.)