OFFSET
1,2
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).
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)
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 *)
PROG
(Sage) [2*n*floor(n/2) for n in (1..50)] # Bruno Berselli, Feb 25 2016
(Maxima) makelist(2*n*floor(n/2), n, 1, 50); /* Bruno Berselli, Feb 25 2016 */
(Magma) [2*n*Floor(n/2): n in [1..50]]; // Bruno Berselli, Feb 25 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Feb 27 2014
STATUS
approved