|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|