|
|
A238411
|
|
a(n) = 2*n*floor(n/2).
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
G.f.: 2*x*(2 + x + x^2)/((1 + x)^2*(1 - x)^3).
a(n) = n*(2*n + (-1)^n - 1)/2.
|
|
MAPLE
|
a := proc (n) options operator, arrow: 2*n*floor((1/2)*n) end proc: seq(a(n), n = 1 .. 70);
|
|
MATHEMATICA
|
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|