Search: id:A003018
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%I A003018 M1178
%S A003018 1,1,2,4,9,20,47,111,270,664,1659,4184,10662,27367,70747,183925,480656,
%T A003018 1261630,3324772,8792592,23327249,62067785,165586565
%N A003018 Number of distinct values taken by 3^3^...^3 (with n 3's and parentheses 
               inserted in all possible ways).
%C A003018 The g.f. (-1+z+6*z**2-3*z**3-8*z**4+3*z**5)/(-1+2*z+6*z**2-9*z**3-10*z**4+9*z**5) 
               conjectured by S. Plouffe in his 1992 dissertation is wrong.
%D A003018 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003018 F. Goebel and R. P. Nederpelt, The number of numerical outcomes of iterated 
               powers, Amer. Math. Monthly, 80 (1971), 1097-1103.
%D A003018 R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the 
               laddered parenthesis. Amer. Math. Monthly 80 (1973), 868-876.
%H A003018 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A003018 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A003018 <a href="Sindx_Par.html#parens">Index entries for sequences related to 
               parenthesizing</a>
%Y A003018 Cf. A002845, A003019, A145545, A145546, A145547, A145548, A145549, A145550, 
               A000081.
%Y A003018 Sequence in context: A130802 A022543 A036618 this_sequence A035084 A058385 
               A058386
%Y A003018 Adjacent sequences: A003015 A003016 A003017 this_sequence A003019 A003020 
               A003021
%K A003018 nonn,nice,more
%O A003018 1,3
%A A003018 N. J. A. Sloane (njas(AT)research.att.com).
%E A003018 a(12) - a(23) from Jon Schoenfield (jonscho(AT)hiwaay.net), Oct 11 2008

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