A228319 - OEIS

%I #24 Nov 16 2024 12:33:11

%S 20,45,82,131,192,265,350,447,556,677,810,955,1112,1281,1462,1655,

%T 1860,2077,2306,2547,2800,3065,3342,3631,3932,4245,4570,4907,5256,

%U 5617,5990,6375,6772,7181,7602,8035,8480,8937,9406,9887,10380

%N The hyper-Wiener index of the graph obtained by applying Mycielski's construction to the star graph K(1,n).

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

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

%F a(n) = 6*n^2 + 7*n + 7.

%F G.f.: x*(20-15*x+7*x^2)/(1-x)^3.

%F The Hosoya-Wiener polynomial is (4*n+1)*t + (2*n^2 + n + 2)*t^2.

%F From _Elmo R. Oliveira_, Nov 15 2024: (Start)

%F E.g.f.: exp(x)*(6*x^2 + 13*x + 7) - 7.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)

%p a := proc (n) options operator, arrow: 6*n^2+7*n+7 end proc: seq(a(n), n = 1 .. 42);

%o (PARI) a(n)=6*n^2+7*n+7 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A228318.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, Aug 27 2013