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 A228318 #25 Nov 16 2024 12:34:44
%S A228318 15,33,59,93,135,185,243,309,383,465,555,653,759,873,995,1125,1263,
%T A228318 1409,1563,1725,1895,2073,2259,2453,2655,2865,3083,3309,3543,3785,
%U A228318 4035,4293,4559,4833,5115,5405,5703,6009
%N A228318 The Wiener index of the graph obtained by applying Mycielski's construction to the star graph K(1,n).
%D A228318 D. B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall, NJ, 2001, p. 205.
%H A228318 H. P. Patil and R. Pandiya Raj, <a href="https://doi.org/10.7151/dmgt.1670">On the total graph of Mycielski graphs, central graphs and their covering numbers</a>, Discussiones Mathematicae Graph Theory, Vol. 33 (2013), pp. 361-371.
%H A228318 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A228318 a(n) = 4*n^2 + 6*n + 5.
%F A228318 G.f.: x*(15-12*x+5*x^2)/(1-x)^3.
%F A228318 The Hosoya-Wiener polynomial is (4*n+1)*t + (2*n^2 + n + 2)*t^2.
%F A228318 From _Elmo R. Oliveira_, Nov 15 2024: (Start)
%F A228318 E.g.f.: exp(x)*(4*x^2 + 10*x + 5) - 5.
%F A228318 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%e A228318 a(1)=15; indeed K(1,1) is the 1-edge graph; the Mycielski construction yields the cycle C(5); its Wiener index is 5*1 + 5*2 = 15.
%p A228318 a := proc (n) options operator, arrow: 4*n^2+6*n+5 end proc; seq(a(n), n = 1 .. 38);
%t A228318 LinearRecurrence[{3,-3,1},{15,33,59},50] (* _Harvey P. Dale_, Jan 13 2022 *)
%o A228318 (PARI) a(n)=4*n^2+6*n+5 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A228318 Cf. A228319.
%K A228318 nonn,easy
%O A228318 1,1
%A A228318 _Emeric Deutsch_, Aug 27 2013