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

Author

Emeric Deutsch, Oct 14 2015

Keywords

• sign
• easy

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(2*n) and one additional center vertex that is adjacent to n vertices of C(2*n) at distances 2 to each other on C(2*n).

The Hosoya polynomial of J_{2,n} is 3*n*x + 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).

Crossrefs

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

Programs

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

Maple

seq((25*n^2 - 39*n)/2, n=0..40);

Mathematica

Table[n (25 n - 39)/2, {n, 0, 40}]

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

Formula

G.f.: x*(32*x-7)/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).