A180571 The Wiener index of the graph \|/_\/_\/_..._\/_\|/ having n nodes on the horizontal path.

58, 136, 259, 436, 676, 988, 1381, 1864, 2446, 3136, 3943, 4876, 5944, 7156, 8521, 10048, 11746, 13624, 15691, 17956, 20428, 23116, 26029, 29176, 32566, 36208, 40111, 44284, 48736, 53476, 58513, 63856, 69514, 75496, 81811, 88468, 95476, 102844, 110581, 118696

Offset

2,1

Comments

The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph.

Links

Table of n, a(n) for n=2..41.

I. Gutman, S.-L. Lee, C.-H. Chu, and Y.-L. Luo, Chemical applications of the Laplacian spectrum of molecular graphs: Studies of the Wiener number, Indian J. Chem., 33A(07) (1994), 603-608.

I. Gutman, W. Linert, I. Lukovits, and Z. Tomović, On the multiplicative Wiener index and its possible chemical applications, Monatshefte für Chemie, 131 (2000), 421-427 (see the equation between (10) and (11); replace n with n+2).

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = (2 + 9*n + 18*n^2 + 3*n^3)/2.

a(n) = Sum_{k >= 0} k*A180570(n,k).

G.f.: z^2*(58 - 96*z + 63*z^2 - 16*z^3)/(1 - z)^4.

Maple

seq((2+9*n+18*n^2+3*n^3)*1/2, n = 2 .. 40);

Crossrefs

Cf. A180570.

Sequence in context: A039536 A348569 A260132 * A044309 A044690 A118153

Adjacent sequences: A180568 A180569 A180570 * A180572 A180573 A180574

Keyword

nonn,easy

Author

Emeric Deutsch, Sep 16 2010

Status

approved