

A198323


MatulaGoebel number of rooted trees that have only vertices of degree 1 and of maximal degree.


0



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 16, 19, 22, 25, 28, 31, 32, 33, 43, 53, 55, 62, 64, 93, 98, 121, 127, 128, 131, 152, 155, 172, 227, 254, 256, 311, 341, 343, 381, 383, 443, 512, 602, 635, 709, 719, 848, 908, 961, 1024, 1397, 1418, 1444, 1619, 1772, 1993, 2048, 2107, 2127, 2939, 3064, 3178, 3209, 3545, 3671, 3698, 3937
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OFFSET

1,2


COMMENTS

The MatulaGoebel number of a rooted tree can be defined in the following recursive manner: to the onevertex tree there corresponds the number 1; to a tree T with root degree 1 there corresponds the tth prime number, where t is the MatulaGoebel number of the tree obtained from T by deleting the edge emanating from the root; to a tree T with root degree m>=2 there corresponds the product of the MatulaGoebel numbers of the m branches of T.


LINKS

Table of n, a(n) for n=1..69.
M. Fischermann, A. Hoffmann, D. Rautenbach, L. SzĂ©kely, and L. Volkmann, Wiener index versus maximum degree in trees, Discrete Applied. Math., 122, 2002, 127137.
F. Goebel, On a 11correspondence between rooted trees and natural numbers, J. Combin. Theory, B 29 (1980), 141143.
I. Gutman and A. Ivic, On Matula numbers, Discrete Math., 150, 1996, 131142.
I. Gutman and YeongNan Yeh, Deducing properties of trees from their Matula numbers, Publ. Inst. Math., 53 (67), 1993, 1722
D. Matula, A natural rooted tree enumeration by prime factorization, SIAM Rev. 10 (1968) 273.
Index entries for sequences related to MatulaGoebel numbers


FORMULA

In A182907 one can find the generating polynomial g(n,x) of the vertices of the rooted tree having MatulaGoebel number n, according to degree. We look for those values of n for which the polynomial g(n) = g(n,x) has at most 2 terms.


EXAMPLE

7 is in the sequence because the rooted tree with MatulaGoebel number 7 is the rooted tree Y, having 3 vertices of degree 1 and 1 vertex of degree 3.
15, 22, and 31 are in the sequence because the corresponding rooted trees are path trees on 6 vertices (with different roots); they have 2 vertices of degree 1 and 4 vertices of degree 2.


CROSSREFS

Cf. A182907.
Sequence in context: A194975 A299441 A069751 * A254649 A261293 A177872
Adjacent sequences: A198320 A198321 A198322 * A198324 A198325 A198326


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Oct 29 2011


STATUS

approved



