A005613 Cascade-realizable Boolean functions of n variables. (Formerly M1982)

2, 2, 10, 114, 1842, 37226, 902570, 25530658, 825345250, 30016622298, 1212957186330, 53916514446482, 2614488320210258, 137345270749953610, 7770078330925987210, 470977659902530345986, 30451167044311817097666, 2091878780326890801618362

Offset

0,1

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=0..17.

E. A. Bender and J. T. Butler, Asymptotic approximations for the number of fanout-free functions, IEEE Trans. Computers, 27 (1978), 1180-1183. (Annotated scanned copy)

J. T. Butler, Letter to N. J. A. Sloane, Jun. 1975 and Dec. 1978.

J. T. Butler, On the number of functions realized by cascades and disjunctive networks, IEEE Trans. Computers, C-24 (1975), 681-690. (Annotated scanned copy)

K. L. Kodandapani and S. C. Seth, On combinational networks with restricted fan-out, IEEE Trans. Computers, 27 (1978), 309-318. (Annotated scanned copy)

Index entries for sequences related to Boolean functions

Formula

a(0) = 2, a(1) = 2, a(n) = Sum_{k=1..n-1} ((-1)^(k+1) * binomial(n,k) * (2^(k+1)+1) * a(n-k)) - (-1)^n(2^n+1)a(1). [From Butler] - Sean A. Irvine, Jul 14 2016

Crossrefs

Sequence in context: A032034 A002250 A304642 * A005616 A005617 A011248

Adjacent sequences: A005610 A005611 A005612 * A005614 A005615 A005616

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Jul 14 2016

a(0) added by Sean A. Irvine, Aug 22 2016

Status

approved