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%I M1178 #42 May 04 2018 23:41:19
%S 1,1,2,4,9,20,47,111,270,664,1659,4184,10662,27367,70747,183925,
%T 480656,1261630,3324772,8792592,23327249,62067785,165586565
%N Number of distinct values taken by 3^3^...^3 (with n 3's and parentheses inserted in all possible ways).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H F. Goebel and R. P. Nederpelt, <a href="http://www.jstor.org/stable/2316312">The number of numerical outcomes of iterated powers</a>, Amer. Math. Monthly, 80 (1971), 1097-1103.
%H R. K. Guy and J. L. Selfridge, <a href="http://www.jstor.org/stable/2319392">The nesting and roosting habits of the laddered parenthesis</a>, Amer. Math. Monthly 80 (8) (1973), 868-876.
%H R. K. Guy and J. L. Selfridge, <a href="/A003018/a003018.pdf">The nesting and roosting habits of the laddered parenthesis</a> (annotated cached copy)
%H <a href="/index/Par#parens">Index entries for sequences related to parenthesizing</a>
%H <a href="http://mathoverflow.net/questions/79442/number-of-distinct-values-taken-by-xx-x-with-parentheses-inserted-in-all-pos">MathOverflow discussion of related questions</a>
%Y Cf. A002845, A003019, A145545, A145546, A145547, A145548, A145549, A145550, A000081.
%K nonn,nice,more
%O 1,3
%A _N. J. A. Sloane_
%E a(12)-a(23) from _Jon E. Schoenfield_, Oct 11 2008
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