cp's OEIS Frontend

A005613 Cascade-realizable Boolean functions of n variables.

%I A005613 M1982 #36 Oct 04 2017 00:04:28
%S A005613 2,2,10,114,1842,37226,902570,25530658,825345250,30016622298,
%T A005613 1212957186330,53916514446482,2614488320210258,137345270749953610,
%U A005613 7770078330925987210,470977659902530345986,30451167044311817097666,2091878780326890801618362
%N A005613 Cascade-realizable Boolean functions of n variables.
%D A005613 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005613 E. A. Bender and J. T. Butler, <a href="/A005612/a005612.pdf">Asymptotic approximations for the number of fanout-free functions</a>, IEEE Trans. Computers, 27 (1978), 1180-1183. (Annotated scanned copy)
%H A005613 J. T. Butler, Letter to N. J. A. Sloane, <a href="/A006447/a006447.pdf">Jun. 1975</a> and <a href="/A005607/a005607_1.pdf">Dec. 1978</a>.
%H A005613 J. T. Butler, <a href="http://dx.doi.org/10.1109/T-C.1975.224288">On the number of functions realized by cascades and disjunctive networks</a>, IEEE Trans. Computers, C-24 (1975), 681-690. (<a href="/A005613/a005613.pdf">Annotated scanned copy</a>)
%H A005613 K. L. Kodandapani and S. C. Seth, <a href="http://doi.ieeecomputersociety.org/10.1109/TC.1978.1675103">On combinational networks with restricted fan-out</a>, IEEE Trans. Computers, 27 (1978), 309-318. (<a href="/A005736/a005736.pdf">Annotated scanned copy</a>)
%H A005613 <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>
%F A005613 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
%K A005613 nonn
%O A005613 0,1
%A A005613 _N. J. A. Sloane_
%E A005613 More terms from _Sean A. Irvine_, Jul 14 2016
%E A005613 a(0) added by _Sean A. Irvine_, Aug 22 2016