This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A198323 Matula-Goebel 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Matula-Goebel number of a rooted tree can be defined in the following recursive manner: to the one-vertex tree there corresponds the number 1; to a tree T with root degree 1 there corresponds the t-th prime number, where t is the Matula-Goebel 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 Matula-Goebel numbers of the m branches of T. LINKS M. Fischermann, A. Hoffmann, D. Rautenbach, L. SzĂ©kely, and L. Volkmann, Wiener index versus maximum degree in trees, Discrete Applied. Math., 122, 2002, 127-137. 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. I. Gutman and Yeong-Nan Yeh, Deducing properties of trees from their Matula numbers, Publ. Inst. Math., 53 (67), 1993, 17-22 D. Matula, A natural rooted tree enumeration by prime factorization, SIAM Rev. 10 (1968) 273. FORMULA In A182907 one can find the generating polynomial g(n,x) of the vertices of the rooted tree having Matula-Goebel 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 Matula-Goebel 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 20 23:20 EST 2019. Contains 319343 sequences. (Running on oeis4.)