|
|
A158681
|
|
Wiener indexes of the complete binary trees with n levels, root being at level 0.
|
|
1
|
|
|
4, 48, 368, 2304, 12864, 66816, 330496, 1579008, 7353344, 33583104, 151056384, 671219712, 2953068544, 12885491712, 55835820032, 240520790016, 1030797656064, 4398058045440, 18691721789440, 79164887531520, 334251639701504, 1407375101657088, 5910974963908608
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
REFERENCES
|
R.Balakrishnan, K.Viswanathan Iyer, K.T.Raghavendra, "Wiener index of two special trees", MATCH Commun. Math. Comput. Chem., 57(2), 2007, 385-392.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (n+4)2^(n+1) + (n-2)2^(2n+2), n>0.
G.f.: 4*x / ( (4*x-1)^2*(2*x-1)^2 ). [From R. J. Mathar, Sep 15 2010]
|
|
EXAMPLE
|
For n=1, the complete binary tree with level 1 is P_{3} whose Wiener index is 4.
|
|
MATHEMATICA
|
LinearRecurrence[{12, -52, 96, -64}, {4, 48, 368, 2304}, 40] (* Harvey P. Dale, Nov 05 2015 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|