|
| |
|
|
A005608
|
|
Number of Boolean functions realized by cascades of n gates.
(Formerly M5476)
|
|
2
|
|
|
|
729, 47601, 3450897, 252034065, 18416334609, 1345741836561, 98337982792977, 7185895596690705, 525098182736403729, 38370735838630837521, 2803882049628099984657, 204889334969084697296145, 14971970589722490394623249
(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..13.
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.
Index entries for sequences related to Boolean functions
|
|
|
FORMULA
|
a(n) = N(n,3,2) where N(n,s,r) = Sum_{i=1..s} S(n,i,s,r) with S(1,i,s,r) = binomial(s,i) * Sum_{k=0..i} (-1)^k * binomial(i,k) * (i-k)^(s*r) and, for n>1, S(n,i,s,r) = Sum_{j=1..s} (S(n-1,j,s,r)/binomial(s,j)) * binomial(s,i) * Sum_{k=0..i-1} (-1)^k * binomial(i,k) * binomial((i-k)^r,j). [From Butler] - Sean A. Irvine, Jul 13 2016
|
|
|
CROSSREFS
|
Cf. A005609, A005618.
Sequence in context: A224016 A059978 A223208 * A233025 A224314 A224378
Adjacent sequences: A005605 A005606 A005607 * A005609 A005610 A005611
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
EXTENSIONS
|
More terms from Sean A. Irvine, Jul 13 2016
|
|
|
STATUS
|
approved
|
| |
|
|
