This site is supported by donations to The OEIS Foundation.



Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A003018 Number of distinct values taken by 3^3^...^3 (with n 3's and parentheses inserted in all possible ways).
(Formerly M1178)
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; refs; listen; history; text; internal format)



N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=1..23.

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 (8) (1973), 868-876.

R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the laddered parenthesis (annotated cached copy)

Index entries for sequences related to parenthesizing

MathOverflow discussion of related questions


Cf. A002845, A003019, A145545, A145546, A145547, A145548, A145549, A145550, A000081.

Sequence in context: A130802 A022543 A036618 * A196244 A035084 A213905

Adjacent sequences:  A003015 A003016 A003017 * A003019 A003020 A003021




N. J. A. Sloane


a(12)-a(23) from Jon E. Schoenfield, Oct 11 2008



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 17 00:41 EST 2018. Contains 318191 sequences. (Running on oeis4.)