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Wedderburn-Etherington number
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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(x2) = 2ax + g(x)]2" Ann. Math. 24 (1923): 121 - 140
External links
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