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

Author

Emeric Deutsch, Sep 16 2010

Keywords

• nonn
• easy

Comments

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

Links

• 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).

Crossrefs

Cf. A180570.

Programs

Maple

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

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.