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 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 6 10:32 EST 2023. Contains 367600 sequences. (Running on oeis4.)