Wedderburn-Etherington number

Wedderburn-Etherington number

In graph theory, the Wedderburn-Etherington numbers count how many weakly 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.

The first Wedderburn-Etherington numbers that are primes are

:2, 3, 11, 23, 983, 2179, 24631, 3626149, 253450711, 596572387.

References

* 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 g(x^2) = 2ax + [ g(x) ] ^2" "Ann. Math." 24 (1923): 121 - 140

External links

*
* (prime subsequence)


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