A158681 Wiener indexes of the complete binary trees with n levels, root being at level 0.

4, 48, 368, 2304, 12864, 66816, 330496, 1579008, 7353344, 33583104, 151056384, 671219712, 2953068544, 12885491712, 55835820032, 240520790016, 1030797656064, 4398058045440, 18691721789440, 79164887531520, 334251639701504, 1407375101657088, 5910974963908608

Offset: 1

Author

K.V.Iyer, Mar 24 2009

Keywords

• nonn
• easy

Examples

			For n=1, the complete binary tree with level 1 is P_{3} whose Wiener index is 4.
		

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

• Index entries for linear recurrences with constant coefficients, signature (12,-52,96,-64).

Programs

Mathematica

LinearRecurrence[{12,-52,96,-64},{4,48,368,2304},40] (* Harvey P. Dale, Nov 05 2015 *)

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]