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Search: id:A003018
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| A003018 |
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Number of distinct values taken by 3^3^...^3 (with n 3's and parentheses inserted in all possible ways).
(Formerly M1178)
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+0
11
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| 1, 1, 2, 4, 9, 20, 47, 111, 270, 664, 1659, 4184, 10662, 27367, 70747, 183925, 480656, 1261630, 3324772, 8792592, 23327249, 62067785, 165586565
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
F. Goebel and R. P. Nederpelt, The number of numerical outcomes of iterated powers, Amer. Math. Monthly, 80 (1971), 1097-1103.
R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the laddered parenthesis. Amer. Math. Monthly 80 (1973), 868-876.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index entries for sequences related to parenthesizing
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CROSSREFS
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Cf. A002845, A003019, A145545, A145546, A145547, A145548, A145549, A145550, A000081.
Sequence in context: A130802 A022543 A036618 this_sequence A035084 A058385 A058386
Adjacent sequences: A003015 A003016 A003017 this_sequence A003019 A003020 A003021
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KEYWORD
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nonn,nice,more
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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a(12) - a(23) from Jon Schoenfield (jonscho(AT)hiwaay.net), Oct 11 2008
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