A238411 - OEIS

%I #14 Sep 08 2022 08:46:07

%S 0,4,6,16,20,36,42,64,72,100,110,144,156,196,210,256,272,324,342,400,

%T 420,484,506,576,600,676,702,784,812,900,930,1024,1056,1156,1190,1296,

%U 1332,1444,1482,1600,1640,1764,1806,1936,1980,2116,2162,2304,2352,2500

%N a(n) = 2*n*floor(n/2).

%C 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 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 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 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).

%F From _Bruno Berselli_, Feb 25 2016: (Start)

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

%F a(n) = n*(2*n + (-1)^n - 1)/2.

%F a(n+1) = 2*A093353(n). (End)

%p a := proc (n) options operator, arrow: 2*n*floor((1/2)*n) end proc: seq(a(n), n = 1 .. 70);

%t Table[2 n Floor[n/2], {n, 1, 50}] (* _Bruno Berselli_, Feb 25 2016 *)

%o (Sage) [2*n*floor(n/2) for n in (1..50)] # _Bruno Berselli_, Feb 25 2016

%o (Maxima) makelist(2*n*floor(n/2), n, 1, 50); /* _Bruno Berselli_, Feb 25 2016 */

%o (Magma) [2*n*Floor(n/2): n in [1..50]]; // _Bruno Berselli_, Feb 25 2016

%Y Cf. A093353.

%K nonn,easy

%O 1,2

%A _Emeric Deutsch_, Feb 27 2014