OFFSET
0,2
COMMENTS
For n>=3, a(n) = the hyper-Wiener index of the Jahangir graph J_{2,n}. The Jahangir graph J_{2,n} is a connected graph consisting of a cycle graph C(2n) and one additional center vertex that is adjacent to n vertices of C(2n) at distances 2 to each other on C(2n).
The Hosoya polynomial of J_{2,n} is 3nx + n(n+3))x^2/2 + n(n-2)x^3 +n(n-3)x^4/2.
REFERENCES
M. R. Farahani, Hosoya polynomial and Wiener index of Jahangir graphs J_{2,m}, Pacific J. Appl. Math, 7 (3), 2015.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: x*(32*x-7)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
MAPLE
seq((25*n^2 - 39*n)/2, n=0..40);
MATHEMATICA
Table[n (25 n - 39)/2, {n, 0, 40}]
PROG
(PARI) vector(50, n, n--; n*(25*n-39)/2)
(PARI) concat(0, Vec(x*(32*x-7)/(1-x)^3 + O(x^100))) \\ Altug Alkan, Oct 18 2015
(Haskell)
a263231 n = n * (25 * n - 39) `div` 2
a263231_list = 0 : -7 : 11 : zipWith (+) a263231_list
(map (* 3) $ tail $ zipWith (-) (tail a263231_list) a263231_list)
-- Reinhard Zumkeller, Nov 04 2015
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Emeric Deutsch, Oct 14 2015
STATUS
approved