Wedderburn–Etherington number

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 nodes. The first few Wedderburn–Etherington numbers are

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,... (sequence A001190 in OEIS)

References

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