A005619 Number of Boolean functions realized by n-input cascades. (Formerly M5020)

16, 240, 6448, 187184, 5474096, 160196400, 4688357168, 137211717424, 4015706384176, 117525666899760, 3439564830058288, 100664021209884464, 2946083492311639856, 86221550057181718320, 2523402922444883797808, 73851169513661744064304

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; arXiv:0911.4975 [math.NT], 2009.

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

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Jul 20 2016

Status

approved