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A180571
The Wiener index of the graph \|/_\/_\/_..._\/_\|/ having n nodes on the horizontal path.
1
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
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).
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Sep 16 2010
STATUS
approved