A003018 Number of distinct values taken by 3^3^...^3 (with n 3's and parentheses inserted in all possible ways).

1, 1, 2, 4, 9, 20, 47, 111, 270, 664, 1659, 4184, 10662, 27367, 70747, 183925, 480656, 1261630, 3324772, 8792592, 23327249, 62067785, 165586565

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• more

References

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

Links

• 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

Crossrefs

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

Extensions

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