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%I #13 Jan 13 2022 19:49:30
%S 15,33,59,93,135,185,243,309,383,465,555,653,759,873,995,1125,1263,
%T 1409,1563,1725,1895,2073,2259,2453,2655,2865,3083,3309,3543,3785,
%U 4035,4293,4559,4833,5115,5405,5703,6009
%N The Wiener index of the graph obtained by applying Mycielski's construction to the star graph K(1,n).
%D H. P. Patil, R. Pandiya Raj, On the total graph of Mycielski graphs. central graphs and their covering numbers, Discussiones Math., Graph Theory, 33,2013, 361-371.
%D D. B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall, NJ, 2001, p. 205.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 4n^2 + 6n + 5.
%F G.f.: x*(15-12*x+5*x^2)/(1-x)^3.
%F The Hosoya-Wiener polynomial is (4n+1)t + (2n^2 + n + 2)t^2.
%e 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 a := proc (n) options operator, arrow: 4*n^2+6*n+5 end proc; seq(a(n), n = 1 .. 38);
%t LinearRecurrence[{3,-3,1},{15,33,59},50] (* _Harvey P. Dale_, Jan 13 2022 *)
%o (PARI) a(n)=4*n^2+6*n+5 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A228319.
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, Aug 27 2013
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