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A005608 Number of Boolean functions realized by cascades of n gates.
(Formerly M5476)
2

%I M5476 #28 Oct 04 2017 00:49:51

%S 729,47601,3450897,252034065,18416334609,1345741836561,98337982792977,

%T 7185895596690705,525098182736403729,38370735838630837521,

%U 2803882049628099984657,204889334969084697296145,14971970589722490394623249

%N Number of Boolean functions realized by cascades of n gates.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H J. T. Butler, <a href="/A005607/a005607.pdf">Fanout-free networks of multivalued gates</a>, Proc. Internat. Symposium Multiple-Valued Logic, Charlotte, NC, 1977, IEEE Press, NY (1977), 39-46. (Annotated scanned copy)

%H J. T. Butler, <a href="/A005607/a005607_1.pdf">Letter to N. J. A. Sloane, Dec. 1978</a>.

%H <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>

%F 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

%Y Cf. A005609, A005618.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Jul 13 2016

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)