The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”). Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A191517 Maximum edge-degree in the rooted tree with Matula-Goebel number n. 0
 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 4, 2, 3, 3, 4, 3, 3, 2, 4, 2, 3, 3, 4, 4, 4, 3, 4, 3, 4, 4, 3, 3, 3, 3, 5, 3, 3, 3, 4, 4, 4, 2, 5, 4, 3, 3, 4, 4, 2, 4, 5, 3, 3, 4, 3, 3, 4, 4, 5, 4, 4, 3, 5, 3, 4, 3, 5, 4, 3, 3, 5, 3, 4, 3, 4, 5, 4, 3, 4, 2, 3, 4, 6, 3, 4, 3, 4, 4, 3, 4, 5, 4, 5, 5, 5, 3, 3, 4, 6, 4, 5, 3, 4, 4, 3, 3, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,4 COMMENTS The degree of an edge is the number of edges adjacent to it. 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. REFERENCES A. T. Balaban, Chemical graphs, Theoret. Chim. Acta (Berl.) 53, 355-375, 1979. 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. W. Matula, A natural rooted tree enumeration by prime factorization, SIAM Review, 10, 1968, 273. R. Todeschini and V. Consonni, Handbook of Molecular Descriptors, Wiley-VCH, 2000. LINKS E. Deutsch, Rooted tree statistics from Matula numbers, arXiv:1111.4288 FORMULA In A191516 one finds the generating polynomial f(n)=F(n,x) of the edges of the rooted tree with Matula-Goebel number n, with respect to edge-degree. a(n)=degree of this polynomial. EXAMPLE a(7)=2 because the rooted tree with Matula-Goebel number 7 is Y; all edges have degree 2. MAPLE with(numtheory): f := proc (n) local r, s, g, h: r := proc (n) options operator, arrow: op(1, factorset(n)) end proc: s := proc (n) options operator, arrow: n/r(n) end proc: g := proc (n) if n = 1 then 0 elif bigomega(n) = 1 then x^bigomega(pi(n)) else x^bigomega(s(n))*g(r(n))+x^bigomega(r(n))*g(s(n)) end if end proc: h := proc (n) if n = 1 then 0 elif bigomega(n) = 1 then x*g(pi(n))+h(pi(n)) else h(r(n))+h(s(n)) end if end proc: sort(expand(g(n)+h(n))) end proc: seq(degree(f(n)), n = 2 .. 120); CROSSREFS Sequence in context: A177227 A174373 A232270 * A303370 A082528 A055980 Adjacent sequences:  A191514 A191515 A191516 * A191518 A191519 A191520 KEYWORD nonn AUTHOR Emeric Deutsch, Dec 15 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 December 5 23:38 EST 2021. Contains 349558 sequences. (Running on oeis4.)