A263226 a(n) = 15*n^2 - 13*n.

0, 2, 34, 96, 188, 310, 462, 644, 856, 1098, 1370, 1672, 2004, 2366, 2758, 3180, 3632, 4114, 4626, 5168, 5740, 6342, 6974, 7636, 8328, 9050, 9802, 10584, 11396, 12238, 13110, 14012, 14944, 15906, 16898, 17920, 18972, 20054, 21166, 22308, 23480, 24682, 25914

Offset: 0

Author

Emeric Deutsch, Oct 12 2015

Keywords

• nonn
• easy

Comments

For n>=3, a(n) = the 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, A263227, A263228, A263229, A263231.

Programs

Magma

[15*n^2-13*n: n in [0..50]]; // Bruno Berselli, Oct 15 2015

Maple

seq(15*n^2-13*n, n = 0 .. 40);

Mathematica

Table[15 n^2 - 13 n, {n, 0, 40}] (* Vincenzo Librandi, Oct 13 2015 *)
LinearRecurrence[{3,-3,1},{0,2,34},50] (* Harvey P. Dale, Jul 27 2018 *)

PARI

vector(50, n, n--; 15*n^2 - 13*n) \\ Altug Alkan, Oct 12 2015

Formula

G.f.: 2*x*(1 + 14*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