Wedderburn–Etherington Number

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In graph theory, the **Wedderburn–Etherington numbers**, named for Ivor Malcolm Haddon Etherington and Joseph Wedderburn, count how many weak binary trees can be constructed: that is, the number of trees for which each graph vertex (not counting the root) is adjacent to no more than three other such vertices, for a given number of node. The first few Wedderburn–Etherington numbers are

## References

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- 1, 1, 1, 2, 3, 6, 11, 23, 46, 98, 207, 451, 983, 2179, 4850, 10905, 24631, 56011, 127912, 293547, 676157, 1563372, 3626149, 8436379, 19680277, 46026618, 107890609, 253450711, 596572387, 1406818759, 3323236238, 7862958391,...

- S. J. Cyvin et al., "Enumeration of constitutional isomers of polyenes,"
*J. Molec. Structure (Theochem)***357**(1995): 255–261 - I. M. H. Etherington, "Non-associate powers and a functional equation,"
*Math. Gaz.***21**(1937): 36–39, 153 - I. M. H. Etherington, "On non-associative combinations,"
*Proc. Royal Soc. Edinburgh*,**59**2 (1939): 153–162. - S. R. Finch,
*Mathematical Constants*. Cambridge: Cambridge University Press (2003): 295–316 - F. Murtagh, "Counting dendrograms: a survey,"
*Discrete Applied Mathematics***7**(1984): 191–199 - J. H. M. Wedderburn, "The functional equation <math>g(x^2) = 2ax + ^2</math>"
*Ann. Math.***24**(1923): 121–140

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