A192025 The Wiener index of the double-comb graph \/_\/_\/...\/_\/ with 3n (n>=1) nodes. The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices in the graph.

4, 29, 84, 178, 320, 519, 784, 1124, 1548, 2065, 2684, 3414, 4264, 5243, 6360, 7624, 9044, 10629, 12388, 14330, 16464, 18799, 21344, 24108, 27100, 30329, 33804, 37534, 41528, 45795, 50344, 55184, 60324, 65773, 71540, 77634, 84064, 90839, 97968, 105460

Offset

1,1

Comments

a(n) = Sum(k*A192024(n,k),k>=1).

Links

Table of n, a(n) for n=1..40.

T. Mansour, M. Schork, The vertex PI index and Szeged index of bridge graphs, Discrete Appl. Math., 157, 2009, 1600-1606 (see last page).

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

Formula

a(n) = n*(3*n^2+12*n-7)/2.

G.f.: x*(4+13*x-8*x^2)/(1-x)^4.

Example

a(2)=29 because in the graph \/_\/ there are 5 pairs of nodes at distance 1, 6 pairs at distance 2, and 4 pairs at distance 3 (5*1 + 6*2 + 4*3 = 29).

Maple

a := n -> (1/2)*n*(3*n^2+12*n-7): seq(a(n), n = 1 .. 40);

Crossrefs

Cf. A192024

Sequence in context: A280854 A042379 A184301 * A288542 A024394 A199399

Adjacent sequences: A192022 A192023 A192024 * A192026 A192027 A192028

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 25 2011

Status

approved