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

0, 4, 6, 16, 20, 36, 42, 64, 72, 100, 110, 144, 156, 196, 210, 256, 272, 324, 342, 400, 420, 484, 506, 576, 600, 676, 702, 784, 812, 900, 930, 1024, 1056, 1156, 1190, 1296, 1332, 1444, 1482, 1600, 1640, 1764, 1806, 1936, 1980, 2116, 2162, 2304, 2352, 2500

Offset: 1

Author

Emeric Deutsch, Feb 27 2014

Keywords

• nonn
• easy

Comments

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.

Links

• M. J. Morgan, S. Mukwembi and H. C. Swart, On the eccentric connectivity index of a graph, Discrete Math., 311, 2011, 1229-1234.
• B. Zhou and Zh. Du, On eccentric connectivity index, Comm. Math. Comp. Chem. (MATCH), 63, 2010, 181-198.
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A093353.

Programs

Magma

[2*n*Floor(n/2): n in [1..50]]; // Bruno Berselli, Feb 25 2016

Maple

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

Mathematica

Table[2 n Floor[n/2], {n, 1, 50}] (* Bruno Berselli, Feb 25 2016 *)

Maxima

makelist(2*n*floor(n/2), n, 1, 50); /* Bruno Berselli, Feb 25 2016 */

Sage

[2*n*floor(n/2) for n in (1..50)] # Bruno Berselli, Feb 25 2016

Formula

From Bruno Berselli, Feb 25 2016: (Start)

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

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

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