A193395 Wiener index of a benzenoid consisting of a double-step zig-zag chain of n hexagons (n >= 2, s = 2123; see the Gutman et al. reference).

109, 271, 553, 971, 1573, 2375, 3425, 4739, 6365, 8319, 10649, 13371, 16533, 20151, 24273, 28915, 34125, 39919, 46345, 53419, 61189, 69671, 78913, 88931, 99773, 111455, 124025, 137499, 151925, 167319, 183729, 201171, 219693, 239311, 260073, 281995, 305125, 329479, 355105

Offset

2,1

Links

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

A. A. Dobrynin, I. Gutman, S. Klavzar, and 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 (3,-2,-2,3,-1).

Formula

a(n) = (16*n^3 + 24*n^2 + 74*n +6*(-1)^n - 51)/3.

G.f.: x^2*(109 - 56*x - 42*x^2 + 72*x^3 - 19*x^4)/((1+x)*(1-x)^4). - Bruno Berselli, Jul 27 2011

Maple

a := proc (n) options operator, arrow; (16/3)*n^3+8*n^2+(74/3)*n+2*(-1)^n-17 end proc: seq(a(n), n = 2 .. 40);

Mathematica

Table[(16n^3+24n^2+74n+6(-1)^n-51)/3, {n, 2, 40}] (* or *) LinearRecurrence[ {3, -2, -2, 3, -1}, {109, 271, 553, 971, 1573}, 40] (* Harvey P. Dale, Apr 08 2020 *)

Prog

(Magma) [(16*n^3 + 24*n^2 + 74*n +6*(-1)^n - 51)/3: n in [2..40]]; // Vincenzo Librandi, Jul 26 2011
(PARI) a(n)=(16*n^3+24*n^2+74*n+6*(-1)^n)/3-17 \\ Charles R Greathouse IV, Jul 28 2011

Crossrefs

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

Sequence in context: A260010 A142144 A193397 * A140036 A031419 A183349

Adjacent sequences: A193392 A193393 A193394 * A193396 A193397 A193398

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 25 2011

Status

approved