A263227 a(n) = n*(67*n - 89)/2.

0, -11, 45, 168, 358, 615, 939, 1330, 1788, 2313, 2905, 3564, 4290, 5083, 5943, 6870, 7864, 8925, 10053, 11248, 12510, 13839, 15235, 16698, 18228, 19825, 21489, 23220, 25018, 26883, 28815, 30814, 32880, 35013, 37213, 39480, 41814, 44215, 46683, 49218, 51820

Offset: 0

Author

Emeric Deutsch, Oct 12 2015

Keywords

• sign
• easy

Comments

For n>=3, a(n) = the hyper-Wiener index of the Jahangir graph J_{3,n}. The Jahangir graph J_{3,n} is a connected graph consisting of a cycle graph C(3n) and one additional center vertex that is adjacent to n vertices of C(3n) at distances 3 to each other on C(3n).

The Hosoya polynomial of J_(3,n) is 4nx + (1/2)n(n+9)x^2 + 2n(n-1)x^3 + n(2n-5)x^4.

Links

• M. R. Farahani, The Wiener index and Hosoya polynomial of a class of Jahangir graphs J_{3,m}, Fundamental J. Math. and Math. Sci., 3 (1), 91-96, 2015.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A049598, A263226, A263228, A263229, A263231.

Programs

Magma

[n*(67*n-89)/2: n in [0..40]]; // Bruno Berselli, Oct 15 2015

Maple

seq((1/2)*n*(67*n-89), n = 0 .. 40);

Mathematica

Table[n (67 n - 89)/2, {n, 0, 40}] (* Vincenzo Librandi, Oct 13 2015 *)

PARI

vector(50, n, n--; n*(67*n-89)/2) \\ Altug Alkan, Oct 12 2015

Formula

G.f.: x*(-11+78*x)/(1-x)^3. - Vincenzo Librandi, Oct 13 2015

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Oct 13 2015