cp's OEIS Frontend

A238411 a(n) = 2*n*floor(n/2).

%I A238411 #14 Sep 08 2022 08:46:07
%S A238411 0,4,6,16,20,36,42,64,72,100,110,144,156,196,210,256,272,324,342,400,
%T A238411 420,484,506,576,600,676,702,784,812,900,930,1024,1056,1156,1190,1296,
%U A238411 1332,1444,1482,1600,1640,1764,1806,1936,1980,2116,2162,2304,2352,2500
%N A238411 a(n) = 2*n*floor(n/2).
%C A238411 For n>=3, a(n) = the eccentric connectivity index of the cycle C[n] on n vertices. The eccentric connectivity index of a simple connected graph G is defined as the sum over all vertices i of G of the product E(i)D(i), where E(i) is the eccentricity and D(i) is the degree of vertex i. For example, a(6)=36 because each vertex of C[6] has degree 2 and eccentricity 3; 6*2*3 = 36.
%H A238411 M. J. Morgan, S. Mukwembi and H. C. Swart, <a href="http://dx.doi.org/10.1016/j.disc.2009.12.013">On the eccentric connectivity index of a graph</a>, Discrete Math., 311, 2011, 1229-1234.
%H A238411 B. Zhou and Zh. Du, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match63/n1/match63n1_181-198.pdf">On eccentric connectivity index</a>, Comm. Math. Comp. Chem. (MATCH), 63, 2010, 181-198.
%H A238411 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A238411 From _Bruno Berselli_, Feb 25 2016: (Start)
%F A238411 G.f.: 2*x*(2 + x + x^2)/((1 + x)^2*(1 - x)^3).
%F A238411 a(n) = n*(2*n + (-1)^n - 1)/2.
%F A238411 a(n+1) = 2*A093353(n). (End)
%p A238411 a := proc (n) options operator, arrow: 2*n*floor((1/2)*n) end proc: seq(a(n), n = 1 .. 70);
%t A238411 Table[2 n Floor[n/2], {n, 1, 50}] (* _Bruno Berselli_, Feb 25 2016 *)
%o A238411 (Sage) [2*n*floor(n/2) for n in (1..50)] # _Bruno Berselli_, Feb 25 2016
%o A238411 (Maxima) makelist(2*n*floor(n/2), n, 1, 50); /* _Bruno Berselli_, Feb 25 2016 */
%o A238411 (Magma) [2*n*Floor(n/2): n in [1..50]]; // _Bruno Berselli_, Feb 25 2016
%Y A238411 Cf. A093353.
%K A238411 nonn,easy
%O A238411 1,2
%A A238411 _Emeric Deutsch_, Feb 27 2014