A193397 Wiener index of a benzenoid consisting of a double-step spiral chain of n hexagons (n>=2, s=21; see the Gutman et al. reference).

109, 271, 553, 955, 1541, 2279, 3265, 4435, 5917, 7615, 9689, 12011, 14773, 17815, 21361, 25219, 29645, 34415, 39817, 45595, 52069, 58951, 66593, 74675, 83581, 92959, 103225, 113995, 125717, 137975, 151249, 165091, 180013, 195535, 212201, 229499, 248005, 267175, 287617

Offset

2,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..10000

A. A. Dobrynin, I. Gutman, S. Klavzar, P. Zigert, Wiener Index of Hexagonal Systems , Acta Applicandae Mathematicae 72 (2002), pp. 247-294.

I. Gutman, S. Klavzar, M. Petkovsek, and P. Zigert, On Hosoya polynomials of benzenoid graphs, Comm. Math. Comp. Chem. (MATCH), 43, 2001, 49-66.

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Formula

a(n) = 4*n^3 + 20*n^2 - 12*n + 2*(-1)^n*(n-2) + 21.

G.f.: x^2*(109+53*x-98*x^2+14*x^3+53*x^4-35*x^5)/((1+x)^2*(1-x)^4). - Bruno Berselli, Jul 27 2011

a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6), with a(2)=109, a(3)=271, a(4)=553, a(5)=955, a(6)=1541, a(7)=2279. - Harvey P. Dale, Aug 26 2011

Maple

a := proc (n) options operator, arrow: 4*n^3+20*n^2-12*n+2*(-1)^n*(n-2)+21 end proc: seq(a(n), n = 2 .. 40);

Mathematica

Table[4n^3+20n^2-12n+2(-1)^n(n-2)+21, {n, 2, 40}] (* or *) LinearRecurrence[ {2, 1, -4, 1, 2, -1}, {109, 271, 553, 955, 1541, 2279}, 39] (* Harvey P. Dale, Aug 26 2011 *)

Prog

(Magma) [4*n^3 + 20*n^2 - 12*n + 2*(-1)^n*(n-2) + 21: n in [2..40]]; // Vincenzo Librandi, Jul 26 2011

Crossrefs

Cf. A143937, A143938, A193391, A193392, A193393, A193394, A193395, A193396.

Sequence in context: A063342 A260010 A142144 * A193395 A140036 A031419

Adjacent sequences: A193394 A193395 A193396 * A193398 A193399 A193400

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 25 2011

Status

approved