cp's OEIS Frontend

A180577 The Wiener index of the windmill graph D(6,n). The windmill graph D(m,n) is the graph obtained by taking n copies of the complete graph K_m with a vertex in common (i.e., a bouquet of n pieces of K_m graphs).

%I A180577 #20 Apr 03 2025 16:03:38
%S A180577 15,80,195,360,575,840,1155,1520,1935,2400,2915,3480,4095,4760,5475,
%T A180577 6240,7055,7920,8835,9800,10815,11880,12995,14160,15375,16640,17955,
%U A180577 19320,20735,22200,23715,25280,26895,28560,30275,32040,33855,35720,37635,39600,41615,43680,45795
%N A180577 The Wiener index of the windmill graph D(6,n). The windmill graph D(m,n) is the graph obtained by taking n copies of the complete graph K_m with a vertex in common (i.e., a bouquet of n pieces of K_m graphs).
%C A180577 The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph.
%C A180577 The Wiener polynomial of D(m,n) is (1/2)n(m-1)t[(m-1)(n-1)t+m].
%C A180577 The Wiener index of D(m,n) is (1/2)n(m-1)[(m-1)(2n-1)+1].
%C A180577 For the Wiener indices of D(3,n), D(4,n), and D(5,n) see A033991, A152743, and A028994, respectively.
%H A180577 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., Vol. 60, 1996, pp. 959-969.
%H A180577 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WindmillGraph.html">Windmill Graph</a>.
%H A180577 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A180577 a(n) = 5*n*(5*n-2).
%F A180577 G.f.: -5*x*(7*x+3)/(x-1)^3. - _Colin Barker_, Oct 30 2012
%F A180577 From _Elmo R. Oliveira_, Apr 03 2025: (Start)
%F A180577 E.g.f.: 5*exp(x)*x*(3 + 5*x).
%F A180577 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%p A180577 seq(5*n*(-2+5*n), n = 1 .. 40);
%o A180577 (PARI) a(n)=5*n*(5*n-2) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A180577 Cf. A028994, A033991, A152743.
%K A180577 nonn,easy
%O A180577 1,1
%A A180577 _Emeric Deutsch_, Sep 21 2010
%E A180577 More terms from _Elmo R. Oliveira_, Apr 03 2025