|
| |
|
|
A005517
|
|
Smallest label f(T) given to a rooted tree T with n nodes in Matula-Goebel labeling.
(Formerly M0706)
|
|
7
| |
|
|
1, 2, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 625, 1125, 1875, 3125, 5625, 9375, 15625, 28125, 46875, 78125, 140625, 234375, 390625, 703125, 1171875, 1953125, 3515625, 5859375, 9765625, 17578125, 29296875, 48828125
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Let p(1)=2, ... denote the primes. The label f(T) for a rooted tree T is 1 if T has 1 node, otherwise f(T) = Product p(f(T_i)) where the T_i are the subtrees obtained by deleting the root and the edges adjacent to it.
|
|
|
REFERENCES
| F. Goebel, On a 1-1-correspondence between rooted trees and natural numbers, J. Combin. Theory, B 29 (1980), 141-143.
I. Gutman and A. Ivic, On Matula numbers, Discrete Math., 150, 1996, 131-142.
D. W. Matula, A natural rooted tree enumeration by prime factorization, SIAM Review, 10, 1968, 273.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index entries for sequences related to rooted trees
Index entries for sequences related to trees
|
|
|
FORMULA
| a(n+3) = 5*a(n) for n >= 3 under plausible assumptions about growth of prime numbers. - David W. Wilson, Jul 05, 2001.
A091233(n) = (A005518(n)-a(n))+1. - Antti Karttunen (Antti.Karttunen(AT)iki.fi), May 24 2004
|
|
|
MAPLE
| A005517:=(-1-2*z-3*z**2+z**4)/(-1+5*z**3); [Conjectured by S. Plouffe in his 1992 dissertation.]
|
|
|
CROSSREFS
| Cf. A061773. See A005518 for the largest value of f(T).
Sequence in context: A003476 A017989 A017990 * A034063 A034073 A114623
Adjacent sequences: A005514 A005515 A005516 * A005518 A005519 A005520
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
