A263229 a(n) = 4*n*(21*n - 26).

0, -20, 128, 444, 928, 1580, 2400, 3388, 4544, 5868, 7360, 9020, 10848, 12844, 15008, 17340, 19840, 22508, 25344, 28348, 31520, 34860, 38368, 42044, 45888, 49900, 54080, 58428, 62944, 67628, 72480, 77500, 82688, 88044, 93568, 99260, 105120, 111148, 117344, 123708, 130240

Offset

0,2

Comments

For n>=3, a(n) = the hyper-Wiener index of the Jahangir graph J_{4,n}. The Jahangir graph J_{4,n} is a connected graph consisting of a cycle graph C(4n) and one additional center vertex that is adjacent to n vertices of C(4n) at distances 4 to each other on C(4n).

The Hosoya polynomial of J_{4,n} is 5nx + n(n+1))x^2/2 + n(2n+1)x^3 +n(3n-4)x^4 + 2n(n-2)x^5 + n(n-3)x^6/2 (see the Farahani reference, p. 234, last line; however, the expression in Theorem 1, p. 233, is accidentally incorrect).

Links

Table of n, a(n) for n=0..40.

M. R. Farahani, Hosoya polynomial and of Jahangir graphs J_{4,m}, Global J. Math, 3 (1), 232-236, 2015.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f. = 4*x*(47*x-5)/(1-x)^3.

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

Maple

seq(84*n^2 - 104*n, n=0..40);

Mathematica

Table[4 n (21 n - 26), {n, 0, 40}] (* Bruno Berselli, Oct 15 2015 *)

Prog

(Magma) [4*n*(21*n-26): n in [0..20]]; // Vincenzo Librandi, Oct 15 2015
(PARI) vector(50, n, n--; 4*n*(21*n-26)) \\ Altug Alkan, Oct 15 2015

Crossrefs

Cf. A049598, A263226, A263227, A263228, A263231.

Sequence in context: A250421 A073968 A219710 * A125330 A126488 A304507

Adjacent sequences: A263226 A263227 A263228 * A263230 A263231 A263232

Keyword

sign,easy

Author

Emeric Deutsch, Oct 13 2015

Status

approved