A228320 - OEIS

%I #14 May 28 2018 03:42:54

%S 203,280,369,470,583,708,845,994,1155,1328,1513,1710,1919,2140,2373,

%T 2618,2875,3144,3425,3718,4023,4340,4669,5010,5363,5728,6105,6494,

%U 6895,7308,7733,8170,8619,9080,9553,10038,10535,11044,11565

%N The Wiener index of the graph obtained by applying Mycielski's construction to the cycle graph C(n).

%D D. B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall, NJ, 2001, p. 205.

%H R. Balakrishnan, S. F. Raj, <a href="http://dx.doi.org/10.7151/dmgt.1509">The Wiener number of powers of the Mycielskian</a>, Discussiones Math. Graph Theory, 30, 2010, 489-498 (see Theorem 2.1).

%H M. Eliasi, G.Raeisi, B. Taeri, <a href="https://doi.org/10.1016/j.dam.2012.01.014">Wiener index of some graph operations</a>, Discrete Appl. Math., 160, 2012, 1333-1344 (see Example 2.5).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 6n^2 - 13n.

%F G.f.: x^7*(203 - 329*x + 138*x^2)/(1 - x)^3.

%F The Hosoya-Wiener polynomial is conjectured to be 4nt +(1/2)n(n+9)t^2 + n(n-4)t^3 + (1/2)n(n-7)t^4.

%p a := proc (n) options operator, arrow: 6*n^2-13*n end proc: seq(a(n), n = 7 .. 45);

%t DeleteCases[CoefficientList[Series[x^7*(203 - 329 x + 138 x^2)/(1 - x)^3, {x, 0, 45}], x], 0] (* or *)

%t Array[6 #^2 - 13 # &, 39, 7] (* _Michael De Vlieger_, May 27 2018 *)

%o (PARI) a(n)=6*n^2-13*n \\ _Charles R Greathouse IV_, Jun 17 2017

%K nonn,easy

%O 7,1

%A _Emeric Deutsch_, Aug 27 2013