|
|
A143938
|
|
The Wiener index of a benzenoid consisting of a linear chain of n hexagons.
|
|
15
|
|
|
27, 109, 279, 569, 1011, 1637, 2479, 3569, 4939, 6621, 8647, 11049, 13859, 17109, 20831, 25057, 29819, 35149, 41079, 47641, 54867, 62789, 71439, 80849, 91051, 102077, 113959, 126729, 140419, 155061, 170687, 187329, 205019, 223789, 243671
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (1/3)*(16*n^3 + 36*n^2 + 26*n + 3).
G.f.: z*(27+z+5*z^2-z^3)/(1-z)^4.
a(n) = Sum_{k=1,..,2*n+1} k*A143937(n,k).
|
|
EXAMPLE
|
a(1)=27 because in a hexagon we have 6 distances equal to 1, 6 distances equal to 2 and 3 distances equal to 3 (6*1+6*2+3*3=27).
|
|
MAPLE
|
seq((16*n^3+36*n^2+26*n+3)*1/3, n = 1 .. 35)
|
|
MATHEMATICA
|
Table[(1/3)*(16*n^3 + 36*n^2 + 26*n + 3), {n, 1, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {27, 109, 279, 569}, 50] (* G. C. Greubel, Dec 08 2016 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|