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 A180574 #18 Feb 16 2025 08:33:13
%S A180574 27,60,105,174,259,376,513,690,891,1140,1417,1750,2115,2544,3009,3546,
%T A180574 4123,4780,5481,6270,7107,8040,9025,10114,11259,12516,13833,15270,
%U A180574 16771,18400,20097,21930,23835,25884,28009,30286,32643,35160,37761,40530
%N A180574 Wiener index of the n-sunlet graph.
%H A180574 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 A180574 D. Stevanovic, <a href="https://doi.org/10.1016/S0012-365X(00)00277-6">Hosoya polynomial of composite graphs</a>, Discrete Math., 235 (2001), 237-244.
%H A180574 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SunletGraph.html">Sunlet Graph</a>
%H A180574 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WienerIndex.html">Wiener Index</a>
%H A180574 Y.-N. Yeh and I. Gutman, <a href="http://dx.doi.org/10.1016/0012-365X(93)E0092-I">On the sum of all distances in composite graphs</a>, Discrete Math., 135 (1994), 359-365.
%H A180574 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A180574 a(n) = Sum(A180573(n,k),k>=1).
%F A180574 a(n) = n(n^2+4n-2)/2 if n is even; a(n) = n(n^2+4n-3)/2 if n is odd.
%F A180574 a(n) = n*(-5+(-1)^n+8*n+2*n^2)/4. - _Colin Barker_, Oct 31 2012
%F A180574 G.f.: -x^3*(5*x^2-2*x-9)*(2*x^3-3*x^2+3)/((x-1)^4*(x+1)^2). - _Colin Barker_, Oct 31 2012
%F A180574 a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6). - _Eric W. Weisstein_, Sep 07 2017
%p A180574 a := proc (n) if `mod`(n, 2) = 0 then (1/2)*n*(n^2+4*n-2) else (1/2)*n*(n^2+4*n-3) end if end proc: seq(a(n), n = 3 .. 45);
%t A180574 Table[n (-5 + (-1)^n + 2 n (4 + n))/4, {n, 3, 20}]
%t A180574 LinearRecurrence[{2, 1, -4, 1, 2, -1}, {27, 60, 105, 174, 259, 376}, 20]
%t A180574 CoefficientList[Series[(27 + 6 x - 42 x^2 + 12 x^3 + 19 x^4 - 10 x^5)/((-1 + x)^4 (1 + x)^2), {x, 0, 20}], x]
%Y A180574 Cf. A180573.
%K A180574 nonn,easy
%O A180574 3,1
%A A180574 _Emeric Deutsch_, Sep 19 2010