A002844 Number of non-isentropic binary rooted trees with n nodes.

1, 1, 2, 5, 13, 36, 102, 296, 871, 2599, 7830, 23799, 72855, 224455, 695303, 2164491

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• more

Comments

From Richard Guy's 1971 letter: "[Studied by] Helen Alderson, J. H. Conway, etc. at Cambridge. These are rooted trees with two branches at each stage and if A,B,C,D (see drawing [in letter]) are further growths, then one treats (AB)(CD) as equivalent to (AC)(BD) - otherwise one distinguishes left and right. [The sequence gives] the number of equivalence classes of such trees."

References

• R. K. Guy, personal communication.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Tyler Foster, A Noncommutative Version of the Natural Numbers, arXiv:1003.2081 [math.QA], 2010. See D(n) Table 2 p. 3.
• R. K. Guy, Letter to N. J. A. Sloane, June 24 1971: front, back [Annotated scanned copy, with permission] See sequence C.
• N. J. A. Sloane, Winter Fruits: New Problems from the OEIS, Dec. 2016 - Jan. 2017 (Part 1), Jan 26 2017.
• N. J. A. Sloane, Winter Fruits: New Problems from the OEIS, Dec. 2016 - Jan. 2017 (slides)
• Doron Zeilberger, Maple program for A002844
• Index entries for sequences related to rooted trees
• Index entries for sequences related to trees

Crossrefs

Bears a superficial resemblance to A036765.

Extensions

Revised by N. J. A. Sloane, Dec 15 2016

a(11)-a(14) from Doron Zeilberger, Jan 31 2017

a(15)-a(16) from Sean A. Irvine, Sep 29 2023