0,5

Trees are unrooted, nodes are unlabeled. Every node has degree <= 4.

Ignoring stereoisomers means that the children of a node are unordered. They can be permuted in any way and it is still the same tree. See A000628 for the analogous sequence with stereoisomers counted.

In alkanes every carbon has valence exactly 4 and every hydrogen has valence exactly 1. But the trees considered here are just the carbon "skeletons" (with all the hydrogen atoms stripped off) so now each carbon bonds to 1 to 4 other carbons. The degree of each node is then <= 4.

K. Adam, Title?, MNU 1983, 36, 29 (in German).

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N. J. A. Sloane, Maple program and first 60 terms for A000022, A000200, A000598, A000602, A000678

Index entries for sequences related to trees

Index entries for "core" sequences

a(n) = A010372(n) + A010373(n/2) for n even, a(n) = A010372(n) for n odd.

Also equals A000022 + A000200 (n>0), both of which have known generating functions. Also g.f. = A000678(x)-A000599(x)+A000598(x^2) = (x+x^2+2x^3...)-(x^2+x^3+3x^4...)+(1+x^2+x^4+...) = 1+x+x^2+x^3+2x^4+3x^5...

a(6)=5 because hexane has five isomers: n-hexane, 2-methylhexane, 3-methylhexane, 2,2-dimethylhexane, 2,3-dimethylhexane. - Michael Lugo (mtlugo(AT)mit.edu), Mar 15 2003

A000602 := proc(n) if n=0 then RETURN(1) else A000022(n)+A000200(n); fi; end;

Cf. A000598, A000625, A000628, A067608-A067610.

Sequence in context: A047031 A056766 A080091 this_sequence A034790 A047121 A096753

Adjacent sequences: A000599 A000600 A000601 this_sequence A000603 A000604 A000605

nonn,easy,core,nice

N. J. A. Sloane (njas(AT)research.att.com).

Additional comments from Steve Strand (snstrand(AT)comcast.net), Aug 20, 2003.

Kappler reference from Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 15 2005