Search: id:A102866
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%I A102866
%S A102866 1,2,5,16,42,116,310,816,2121,5466,13937,35248,88494,220644,546778,
%T A102866 1347344,3302780,8057344,19568892,47329264,114025786,273709732,
%U A102866 654765342,1561257968,3711373005,8797021714,20794198581,49024480880
%N A102866 Number of finite languages over a binary alphabet (set of binary words 
               of total length n).
%C A102866 Analogous to A034899 (which also enumerates multisets of words)
%H A102866 P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/
               Publications/books.html">Analytic Combinatorics</a>, 2009; see page 
               64
%F A102866 GF: exp(Sum((-1)^(j-1)/j*(2*z^j)/(1-2*z^j), j=1..infinity)):
%e A102866 a(2)=5 because the sets are {a,b}, {aa}, {ab}, {ba}, {bb};
%e A102866 a(3)=16 because the sets are {a,aa}, {a,ab}, {a,ba}, {a,bb}, {b,aa}, 
               {b,ab}, {b,ba}, {b,bb}, {aaa}, {aab}, {aba}, {abb}, {baa}, {bab}, 
               {bba}, {bbb}
%p A102866 series(exp(add((-1)^(j-1)/j*(2*z^j)/(1-2*z^j),j=1..40)),z,40);
%Y A102866 Cf. A034899.
%Y A102866 Sequence in context: A124720 A076958 A163825 this_sequence A148368 A148369 
               A148370
%Y A102866 Adjacent sequences: A102863 A102864 A102865 this_sequence A102867 A102868 
               A102869
%K A102866 nonn
%O A102866 0,2
%A A102866 Philippe Flajolet (Philippe.Flajolet(AT)inria.fr), Mar 01 2005

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