韦德伯恩-埃瑟林顿数

在图论中，韦德伯恩-埃瑟林顿数是由计算每张图有多少弱二叉树问题而得出的数列。

最初的几个韦德伯恩-埃瑟林顿数为： 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,... （OEIS数列A001190）

组合意义上的诠释

奥特树与弱二叉树，两种通过韦德伯恩-埃瑟林顿数计数的有根二叉树。

名字由来

韦德伯恩-埃瑟林顿数的名字由来是两个数学家艾弗·埃瑟林顿和约瑟夫·韦德伯恩。

参考资料

• OEIS.A001190
• 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