OFFSET
1,4
COMMENTS
This is a variation on the terminal Wiener index defined by Gutman, Furtula, and Petrović. Here terminal vertices are taken as the childless vertices, so a(n) is the sum of the path lengths between pairs of childless vertices.
LINKS
Kevin Ryde, Table of n, a(n) for n = 1..10000
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.
Ivan Gutman, Boris Furtula and Miroslav Petrović, Terminal Wiener Index, Journal of Mathematical Chemistry, volume 46, 2009, pages 522-531.
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 and Notes
FORMULA
PROG
(PARI) See links.
CROSSREFS
KEYWORD
nonn
AUTHOR
Kevin Ryde, Nov 05 2021
STATUS
approved