cp's OEIS Frontend

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

%I A002844 M1445 N0571 #48 Sep 29 2023 05:41:51
%S A002844 1,1,2,5,13,36,102,296,871,2599,7830,23799,72855,224455,695303,2164491
%N A002844 Number of non-isentropic binary rooted trees with n nodes.
%C A002844 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."
%D A002844 R. K. Guy, personal communication.
%D A002844 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002844 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002844 Tyler Foster, <a href="https://arxiv.org/abs/1003.2081">A Noncommutative Version of the Natural Numbers</a>, arXiv:1003.2081 [math.QA], 2010. See D(n) Table 2 p. 3.
%H A002844 R. K. Guy, Letter to N. J. A. Sloane, June 24 1971: <a href="/A002572/a002572.jpg">front</a>, <a href="/A002572/a002572_1.jpg">back</a> [Annotated scanned copy, with permission] See sequence C.
%H A002844 N. J. A. Sloane, <a href="https://vimeo.com/201218446">Winter Fruits: New Problems from the OEIS, Dec. 2016 - Jan. 2017 (Part 1)</a>, Jan 26 2017.
%H A002844 N. J. A. Sloane, <a href="/A002844/a002844.pdf">Winter Fruits: New Problems from the OEIS, Dec. 2016 - Jan. 2017 (slides)</a>
%H A002844 Doron Zeilberger, <a href="/A002844/a002844.txt">Maple program for A002844</a>
%H A002844 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H A002844 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%Y A002844 Bears a superficial resemblance to A036765.
%K A002844 nonn,more
%O A002844 1,3
%A A002844 _N. J. A. Sloane_
%E A002844 Revised by _N. J. A. Sloane_, Dec 15 2016
%E A002844 a(11)-a(14) from _Doron Zeilberger_, Jan 31 2017
%E A002844 a(15)-a(16) from _Sean A. Irvine_, Sep 29 2023