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%I #18 Dec 19 2024 11:46:19
%S 1,4,14,49,86,301,1849,454,1589,9761,51529,886,3101,19049,100561,
%T 196249,3986,13951,85699,452411,882899,3972049,31754,111139,682711,
%U 3604079,7033511,31642861,252079129,6418,22463,137987,728443,1421587,6395537,50949293,10297681
%N Matula-Goebel number of the rooted binary tree with Colijn-Plazzotta number n.
%C A permutation of A111299.
%H C. Colijn and G. Plazzotta, <a href="https://doi.org/10.1093/sysbio/syx046">A Metric on Phylogenetic Tree Shapes</a>, Systematic Biology, volume 67, number 1, January 2018, pages 113-126.
%H F. Goebel, <a href="https://doi.org/10.1016/0095-8956(80)90049-0">On a 1-1-Correspondence between Rooted Trees and Natural Numbers</a>, Journal of Combinatorial Theory, series B, volume 29, 1980, pages 141-143.
%H D. W. Matula, <a href="https://doi.org/10.1137/1010054">A Natural Rooted Tree Enumeration By Prime Factorization</a>, SIAM Review, volume 10, number 2, April 1968, page 273 (also <a href="http://www.jstor.org/stable/2027327">at JSTOR</a>).
%H Kevin Ryde, <a href="/A356121/a356121.gp.txt">PARI/GP Code</a>
%H <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>
%F a(n) = prime(a(x)) * prime(a(y)) for n>=2, where subtrees x = A002024(n-1) and y = A002260(n-1).
%o (PARI) \\ See links.
%Y Cf. A002024, A002260, A111299.
%K nonn
%O 1,2
%A _Kevin Ryde_, Jul 31 2022