A005608 Number of Boolean functions realized by cascades of n gates. (Formerly M5476)

729, 47601, 3450897, 252034065, 18416334609, 1345741836561, 98337982792977, 7185895596690705, 525098182736403729, 38370735838630837521, 2803882049628099984657, 204889334969084697296145, 14971970589722490394623249

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