A263231 a(n) = n*(25*n - 39)/2.

0, -7, 11, 54, 122, 215, 333, 476, 644, 837, 1055, 1298, 1566, 1859, 2177, 2520, 2888, 3281, 3699, 4142, 4610, 5103, 5621, 6164, 6732, 7325, 7943, 8586, 9254, 9947, 10665, 11408, 12176, 12969, 13787, 14630, 15498, 16391, 17309, 18252, 19220

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

Cf. A263226, A263227, A263228, A263229, A263230.

Sequence in context: A018508 A038277 A045462 * A077411 A085016 A067690

Adjacent sequences: A263228 A263229 A263230 * A263232 A263233 A263234

Keyword

sign,easy

Author

Emeric Deutsch, Oct 14 2015

Status

approved