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.

[edit] 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

[edit] External links

• (sequence A001190 in OEIS)
• (sequence A136402 in OEIS) (prime subsequence)