|
| |
|
|
A061773
|
|
Triangle in which n-th row lists Matula-Goebel numbers for all rooted trees with n nodes.
|
|
8
| |
|
|
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 19, 15, 18, 20, 21, 22, 23, 24, 26, 28, 29, 31, 32, 34, 37, 38, 41, 43, 53, 59, 67, 25, 27, 30, 33, 35, 36, 39, 40, 42, 44, 46, 47, 48, 49, 51, 52, 56, 57, 58, 61, 62, 64, 68, 71, 73, 74, 76, 79, 82, 83, 86, 89, 101, 106
(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.
n-th row has A000081(n) terms.
First entry in row n is A005517(n).
Last entry in row n is A005518(n).
The Maple program yields row n after defining F = A005517(n) and L = A005518(n).
|
|
|
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.
|
|
|
LINKS
| Index entries for sequences related to rooted trees
Index entries for sequences related to trees
|
|
|
EXAMPLE
| The labels for the rooted trees with at most 4 nodes are as follows (x is the root):
................................o
................................|
..........o.......o.......o...o.o
..........|........\.......\./..|
..o.o...o.o.o.o.o...o...o...o...o
..|..\./..|..\|/.....\./....|...|
x.x...x...x...x.......x.....x...x
1.2...4...3...8.......6.....7...5 (label)
Triangle begins:
1;
2;
3,4;
5,6,7,8;
9,10,11,12,13,14,16,17,19;
15,18,20,21,22,23,24,26,28,29,31,32,34,37,38,41,43,53,59,67;
25,27,30,33,35,36,39,40,42,44,46,47,48,49,51,52,56,57,58,61,62,64,68,\
71,73,74,76,79,82,83,86,89,101,106,107,109,118,127,131,134,139,157,163,\
179,191,241,277,331;
...
|
|
|
MAPLE
| n := 8: F := 45: L := 2221: with(numtheory): N := proc (m) local r, s: r := proc (m) options operator, arrow: op(1, factorset(m)) end proc: s := proc (m) options operator, arrow: m/r(m) end proc: if m = 1 then 1 elif bigomega(m) = 1 then 1+N(pi(m)) else N(r(m))+N(s(m))-1 end if end proc: A := {}: for k from F to L do if N(k) = n then A := `union`(A, {k}) else end if end do: A;
|
|
|
CROSSREFS
| Cf. A061775. Minimal and maximal entries in each row give A005517, A005518.
Sequence in context: A070776 A076564 A179892 * A125007 A035062 A032964
Adjacent sequences: A061770 A061771 A061772 * A061774 A061775 A061776
|
|
|
KEYWORD
| nonn,tabf,nice,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 22 2001
|
|
|
EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 01 2004
|
| |
|
|
