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A002844 Number of non-isentropic binary rooted trees with n nodes.
(Formerly M1445 N0571)
1, 1, 2, 5, 13, 36, 102, 296, 871, 2599, 7830, 23799, 72855, 224455 (list; graph; refs; listen; history; text; internal format)



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."


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).


Table of n, a(n) for n=1..14.

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


Bears a superficial resemblance to A036765.

Sequence in context: A346738 A116409 A279196 * A223096 A277996 A099164

Adjacent sequences: A002841 A002842 A002843 * A002845 A002846 A002847




N. J. A. Sloane


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

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



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Last modified December 9 17:12 EST 2022. Contains 358702 sequences. (Running on oeis4.)