A005613 Cascade-realizable Boolean functions of n variables.
2, 2, 10, 114, 1842, 37226, 902570, 25530658, 825345250, 30016622298, 1212957186330, 53916514446482, 2614488320210258, 137345270749953610, 7770078330925987210, 470977659902530345986, 30451167044311817097666, 2091878780326890801618362
Offset: 0
Keywords
References
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- 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
Extensions
More terms from Sean A. Irvine, Jul 14 2016
a(0) added by Sean A. Irvine, Aug 22 2016