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A356121
Matula-Goebel number of the rooted binary tree with Colijn-Plazzotta number n.
1
1, 4, 14, 49, 86, 301, 1849, 454, 1589, 9761, 51529, 886, 3101, 19049, 100561, 196249, 3986, 13951, 85699, 452411, 882899, 3972049, 31754, 111139, 682711, 3604079, 7033511, 31642861, 252079129, 6418, 22463, 137987, 728443, 1421587, 6395537, 50949293, 10297681
OFFSET
1,2
COMMENTS
A permutation of A111299.
LINKS
C. Colijn and G. Plazzotta, A Metric on Phylogenetic Tree Shapes, Systematic Biology, volume 67, number 1, January 2018, pages 113-126.
F. Goebel, On a 1-1-Correspondence between Rooted Trees and Natural Numbers, Journal of Combinatorial Theory, series B, volume 29, 1980, pages 141-143.
D. W. Matula, A Natural Rooted Tree Enumeration By Prime Factorization, SIAM Review, volume 10, number 2, April 1968, page 273 (also at JSTOR).
Kevin Ryde, PARI/GP Code
FORMULA
a(n) = prime(a(x)) * prime(a(y)) for n>=2, where subtrees x = A002024(n-1) and y = A002260(n-1).
PROG
(PARI) See links.
CROSSREFS
KEYWORD
nonn
AUTHOR
Kevin Ryde, Jul 31 2022
STATUS
approved