This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A186235 #32 Sep 08 2022 08:45:55
%S A186235 10,18,57,82,169,220,374,460,700,830,1175,1358,1827,2072,2684,3000,
%T A186235 3774,4170,5125,5610,6765,7348,8722,9412,11024,11830,13699,14630,
%U A186235 16775,17840,20280,21488,24242,25602,28689,30210,33649,35340,39150,41020
%N A186235 Total Wiener index of double-star trees with n nodes.
%C A186235 For the trees of a given order, it appears that the Wiener indexes are very close. For n=8, the indexes are 54, 57, and 58.
%C A186235 The second Bomfim link refers to formulas of the total Wiener index, and the average Wiener index of those trees.
%H A186235 Vincenzo Librandi, <a href="/A186235/b186235.txt">Table of n, a(n) for n = 4..10000</a>
%H A186235 Rundan Xing, Bo Zho, <a href="http://arxiv.org/abs/1010.5867">Ordering trees having small reverse Wiener indices</a>
%H A186235 W. Bomfim, <a href="http://oeis.org/wiki/File:Figure2.PNG">Example</a>
%H A186235 W. Bomfim, <a href="http://oeis.org/wiki/File:Figure3.png">Formulas</a>
%H A186235 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).
%F A186235 G.f.: x^4*(10+8*x+9*x^2+x^3)/((1+x)^3*(1-x)^4). Also a(n)=(n*(28*n^2-129*n+176)+3*(5*n^2-12*n+8)*(-1)^n-72)/48. - _Bruno Berselli_, Feb 15 2011
%F A186235 For even n, a(n)=(14*n^3-57*n^2+70*n)/24-1, otherwise a(n)=(7*n^3+53*n)/12-3*n^2-2.
%F A186235 With d=floor((n-2)/2), a(n)=d((n-2)*(n-1)+n*(d+3)/2-d^2/3-3*d/2-13/6).
%e A186235 The first Bomfim link shows a way to find a(8).
%t A186235 a[n_]:= a[n] = -a[n-7] + a[n-6] + 3a[n-5] - 3a[n-4] - 3a[n-3] + 3a[n-2] + a[n-1]; a[0]=-1; a[1]=0; a[2]=0; a[3]=0; a[4]=10; a[5]=18; a[6]=57; a /@ Range[4, 43] (* _Jean-François Alcover_, Jun 01 2011, after recurrence signature *)
%t A186235 LinearRecurrence[{1,3,-3,-3,3,1,-1},{10,18,57,82,169,220,374},40] (* _Harvey P. Dale_, Mar 25 2013 *)
%o A186235 (PARI) for(n=4,43,if(n%2,print1((1/12)*(7*n^3+53*n)-3*n^2-2,", "), print1((1/24)*(14*n^3-57*n^2+70*n)-1,", ")))
%o A186235 (Magma)[ IsEven(n) select (n-2)*(2*n-3)*(7*n-4)/24 else (n-3)*(n-1)*(7*n-8)/12: n in [4..43] ]; // _Bruno Berselli_, Feb 17 2011
%Y A186235 Cf. A122681, A140106, A168559.
%K A186235 nonn,easy
%O A186235 4,1
%A A186235 _Washington Bomfim_, Feb 15 2011