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%I #16 Jul 20 2017 02:26:32
%S 27,144,351,648,1035,1512,2079,2736,3483,4320,5247,6264,7371,8568,
%T 9855,11232,12699,14256,15903,17640,19467,21384,23391,25488,27675,
%U 29952,32319,34776,37323,39960,42687,45504,48411,51408,54495,57672,60939
%N The Wiener index of the Dutch windmill graph D(6,n) (n>=1).
%C The Dutch windmill graph D(m,n) (also called friendship graph) is the graph obtained by taking n copies of the cycle graph C_m with a vertex in common (i.e., a bouquet of n C_m graphs).
%C The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph.
%H B. E. Sagan, Y-N. Yeh and P. Zhang, <a href="http://users.math.msu.edu/users/sagan/Papers/Old/wpg-pub.pdf">The Wiener Polynomial of a Graph</a>, Internat. J. of Quantum Chem., 60, 1996, 959-969.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DutchWindmillGraph.html">Dutch Windmill Graph</a>.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = A180867(6,n).
%F a(n) = 9n(5n-2).
%F The Wiener polynomial of the graph D(6,n) is (1/2)nt(t^2+2t+2)((n-1)t^3+2(n-1)t^2+2(n-1)t+6).
%F G.f.: -9*x*(7*x+3)/(x-1)^3. - _Colin Barker_, Oct 31 2012
%e a(1)=27 because in D(6,1)=C_6 we have 6 distances equal to 1, 6 distances equal to 2, and 3 di stances equal to 3.
%p seq(9*n*(5*n-2), n = 1 .. 40);
%o (PARI) a(n)=9*n*(5*n-2) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A033991, A014642, A180579, A180867.
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, Sep 30 2010
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