This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A165910 Wiener indices of Fibonacci trees of order k. 2
 1, 4, 18, 62, 210, 666, 2063, 6226, 18484, 54100, 156620, 449268, 1278981, 3617544, 10175590, 28485218, 79406350, 220536910, 610487875, 1684974790, 4638298536, 12737460744, 34902844728, 95449821672, 260554112425, 710056257196 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Fibonacci trees T(f(k)) of order k is defined as follows: 1. T(f(-1)) and T(f(0)) each consist of a single node. 2. For k >= 1, T(f(k)) is built from copies of T(f(k-1)) and T(f(k-2)) by connecting (by an edge) T(f(k-2)) as the rightmost child of the root of T(f(k-1)). REFERENCES K. Viswanathan Iyer and K. R. Udaya Kumar Reddy, Wiener index of Binomial trees and Fibonacci trees, Int'l. J. Math. Engin. with Comp., Accepted for publication, Sept. 2009. LINKS K. Viswanathan Iyer and K. R. Udaya Kumar Reddy, Wienerindex of binomial trees and Fibonacci trees, arXiv:0910.4432 Index entries for linear recurrences with constant coefficients, signature (5, -3, -14, 10, 14, -5, -3, 1). FORMULA The Wiener index W(T(f(k))) of the Fibonacci tree T(f(k)) satisfies the following recurrence: W(T(f(k))) = W(T(f(k-1))) + W(T(f(k-2))) + F(k+1) D(T(f), (k-2)) + F(k) D(T(f), (k-1)) + F(k+1) F(k), where D(T(f), k) = (1/5) (k F(k+2) + (k+2) F(k)) and F(k) is the k-th Fibonacci number. D(T(f),k) = A001629(k+1). Conjecture: G.f. x*(1-x+x^2-2*x^3)/( (1-x^2-x) * (1+x)^2 * (x^2-3*x+1)^2 ). [From R. J. Mathar, Apr 19 2010] EXAMPLE W(T(1)) = 1 because T(1) is a single edge. W(T(2)) = 4 because T(2) is a path on three vertices. CROSSREFS Sequence in context: A292465 A227162 A057414 * A212766 A100177 A083321 Adjacent sequences:  A165907 A165908 A165909 * A165911 A165912 A165913 KEYWORD nonn AUTHOR K.V.Iyer, K. R. Udaya Kumar Reddy, Sep 30 2009 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 October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)