韋德伯恩-埃瑟林頓數

在圖論中，韋德伯恩-埃瑟林頓數是由計算每張圖有多少弱二叉樹問題而得出的數列。

最初的幾個韋德伯恩-埃瑟林頓數為： 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數列A001190）

組合意義上的詮釋

奧特樹與弱二叉樹，兩種通過韋德伯恩-埃瑟林頓數計數的有根二叉樹。

名字由來

韋德伯恩-埃瑟林頓數的名字由來是兩個數學家艾弗·埃瑟林頓和約瑟夫·韋德伯恩。

參考資料

• 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